90=4x(2x-6)

Solution for 90=4x(2x-6) equation:

90=4x(2x-6)

We move all terms to the left:

90-(4x(2x-6))=0


We calculate terms in parentheses: -(4x(2x-6)), so:

4x(2x-6)

We multiply parentheses

8x^2-24x

Back to the equation:

-(8x^2-24x)


We get rid of parentheses

-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}
$