-8x^2-75x+90=0

Solution for -8x^2-75x+90=0 equation:

-8x^2-75x+90=0

a = -8; b = -75; c = +90;
Δ = b2-4ac
Δ = -752-4·(-8)·90
Δ = 8505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8505}=\sqrt{81*105}=\sqrt{81}*\sqrt{105}=9\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-9\sqrt{105}}{2*-8}=\frac{75-9\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+9\sqrt{105}}{2*-8}=\frac{75+9\sqrt{105}}{-16}
$