90=4x^2-12x

Solution for 90=4x^2-12x equation:

90=4x^2-12x

We move all terms to the left:

90-(4x^2-12x)=0

We get rid of parentheses

-4x^2+12x+90=0

a = -4; b = 12; c = +90;
Δ = b2-4ac
Δ = 122-4·(-4)·90
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{11}}{2*-4}=\frac{-12-12\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{11}}{2*-4}=\frac{-12+12\sqrt{11}}{-8}
$