2x+x(x+10)=90

Solution for 2x+x(x+10)=90 equation:

2x+x(x+10)=90

We move all terms to the left:

2x+x(x+10)-(90)=0

We multiply parentheses

x^2+2x+10x-90=0

We add all the numbers together, and all the variables

x^2+12x-90=0

a = 1; b = 12; c = -90;
Δ = b2-4ac
Δ = 122-4·1·(-90)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{14}}{2*1}=\frac{-12-6\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{14}}{2*1}=\frac{-12+6\sqrt{14}}{2}
$