8x^2-24x=90

Solution for 8x^2-24x=90 equation:

8x^2-24x=90

We move all terms to the left:

8x^2-24x-(90)=0

a = 8; b = -24; c = -90;
Δ = b2-4ac
Δ = -242-4·8·(-90)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{6}}{2*8}=\frac{24-24\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{6}}{2*8}=\frac{24+24\sqrt{6}}{16}
$