Hint Number =

-120t2-40t+1200 = 0

##### Set up the a, b, and c values:

a = -120, b = -40, c = 1200

 t  = -b ± √b2 - 4ac 2a

-b = -(-40)

-b = 40

##### Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = -402 - 4 x -120 x 1200

Δ = 1600 - -576000

Δ = 577600 <--- Discriminant

Since Δ > 0, we expect two real roots.

Δ = √(577600)

Δ = 760

##### -b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = 40 + 760

Numerator 1 = 800

##### -b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = 40 - 760

Numerator 2 = -720

##### Calculate 2a

Denominator = 2 * a

Denominator = 2 * -120

Denominator = -240

##### Find Solutions

 Solution 1  = Numerator 1 Denominator

 Solution 1  = 800 -240

Solution 1 = -3.3333333333333 or 10/-3

##### Solution 2

 Solution 2  = Numerator 2 Denominator

 Solution 2  = -720 -240

Solution 2 = 3

##### Solution Set

(Solution 1, Solution 2) = (-3.3333333333333, 3)

(-3.3333333333333)2 - 40(-3.3333333333333) + 1200 ? 0

(11.111111111111) + 133.333333333331200 ? 0

-1333.3333333333 + 133.333333333331200 ? 0

0 = 0

(3)2 - 40(3) + 1200 ? 0

(9) - 1201200 ? 0

-1080 - 1201200 ? 0

0 = 0

(Solution 1, Solution 2) = (-3.3333333333333, 3)

(Solution 1, Solution 2) = (-3.3333333333333, 3)
##### How does the Quadratic Equations and Inequalities Calculator work?
Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

### What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

### What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the square
a technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + k
equation
a statement declaring two mathematical expressions are equal
factor
a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
intercept
parabola
a plane curve which is approximately U-shaped