-45a^2+250a+120=0

Solution for -45a^2+250a+120=0 equation:

-45a^2+250a+120=0

a = -45; b = 250; c = +120;
Δ = b2-4ac
Δ = 2502-4·(-45)·120
Δ = 84100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{84100}=290$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-290}{2*-45}=\frac{-540}{-90}
=+6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+290}{2*-45}=\frac{40}{-90}
=-4/9
$