90=2x(x-9)

Solution for 90=2x(x-9) equation:

90=2x(x-9)

We move all terms to the left:

90-(2x(x-9))=0


We calculate terms in parentheses: -(2x(x-9)), so:

2x(x-9)

We multiply parentheses

2x^2-18x

Back to the equation:

-(2x^2-18x)


We get rid of parentheses

-2x^2+18x+90=0

a = -2; b = 18; c = +90;
Δ = b2-4ac
Δ = 182-4·(-2)·90
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{29}}{2*-2}=\frac{-18-6\sqrt{29}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{29}}{2*-2}=\frac{-18+6\sqrt{29}}{-4}
$