90=x+2x(x+10)

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

90=x+2x(x+10)

We move all terms to the left:

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


We calculate terms in parentheses: -(x+2x(x+10)), so:

x+2x(x+10)

We multiply parentheses

2x^2+x+20x

We add all the numbers together, and all the variables

2x^2+21x

Back to the equation:

-(2x^2+21x)


We get rid of parentheses

-2x^2-21x+90=0

a = -2; b = -21; c = +90;
Δ = b2-4ac
Δ = -212-4·(-2)·90
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{129}}{2*-2}=\frac{21-3\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{129}}{2*-2}=\frac{21+3\sqrt{129}}{-4}
$