2x(x+9)=90

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

2x(x+9)=90

We move all terms to the left:

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

We multiply 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}
$