-5x^2+55x-120=0

Solution for -5x^2+55x-120=0 equation:

-5x^2+55x-120=0

a = -5; b = 55; c = -120;
Δ = b2-4ac
Δ = 552-4·(-5)·(-120)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-25}{2*-5}=\frac{-80}{-10}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+25}{2*-5}=\frac{-30}{-10}
=+3
$