2x+(x+5)(x+5)=90

Solution for 2x+(x+5)(x+5)=90 equation:

2x+(x+5)(x+5)=90

We move all terms to the left:

2x+(x+5)(x+5)-(90)=0

We multiply parentheses ..

(+x^2+5x+5x+25)+2x-90=0

We get rid of parentheses

x^2+5x+5x+2x+25-90=0

We add all the numbers together, and all the variables

x^2+12x-65=0

a = 1; b = 12; c = -65;
Δ = b2-4ac
Δ = 122-4·1·(-65)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{101}}{2*1}=\frac{-12-2\sqrt{101}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{101}}{2*1}=\frac{-12+2\sqrt{101}}{2}
$