2x(10+x)=90

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

2x(10+x)=90

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(x+10)-90=0

We multiply parentheses

2x^2+20x-90=0

a = 2; b = 20; c = -90;
Δ = b2-4ac
Δ = 202-4·2·(-90)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{70}}{2*2}=\frac{-20-4\sqrt{70}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{70}}{2*2}=\frac{-20+4\sqrt{70}}{4}
$