90=2x(2x+3)

Solution for 90=2x(2x+3) equation:

90=2x(2x+3)

We move all terms to the left:

90-(2x(2x+3))=0


We calculate terms in parentheses: -(2x(2x+3)), so:

2x(2x+3)

We multiply parentheses

4x^2+6x

Back to the equation:

-(4x^2+6x)


We get rid of parentheses

-4x^2-6x+90=0

a = -4; b = -6; c = +90;
Δ = b2-4ac
Δ = -62-4·(-4)·90
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{41}}{2*-4}=\frac{6-6\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{41}}{2*-4}=\frac{6+6\sqrt{41}}{-8}
$