6x(x-8)=90

Solution for 6x(x-8)=90 equation:

6x(x-8)=90

We move all terms to the left:

6x(x-8)-(90)=0

We multiply parentheses

6x^2-48x-90=0

a = 6; b = -48; c = -90;
Δ = b2-4ac
Δ = -482-4·6·(-90)
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{31}}{2*6}=\frac{48-12\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{31}}{2*6}=\frac{48+12\sqrt{31}}{12}
$