(x+10)2x+x=90

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

(x+10)2x+x=90

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+x+20x-90=0

We add all the numbers together, and all the variables

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}
$