6x(x-4)=90

Solution for 6x(x-4)=90 equation:

6x(x-4)=90

We move all terms to the left:

6x(x-4)-(90)=0

We multiply parentheses

6x^2-24x-90=0

a = 6; b = -24; c = -90;
Δ = b2-4ac
Δ = -242-4·6·(-90)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{19}}{2*6}=\frac{24-12\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{19}}{2*6}=\frac{24+12\sqrt{19}}{12}
$