(x+9)(x+9)=85

Solution for (x+9)(x+9)=85 equation:

(x+9)(x+9)=85

We move all terms to the left:

(x+9)(x+9)-(85)=0

We multiply parentheses ..

(+x^2+9x+9x+81)-85=0

We get rid of parentheses

x^2+9x+9x+81-85=0

We add all the numbers together, and all the variables

x^2+18x-4=0

a = 1; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·1·(-4)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{85}}{2*1}=\frac{-18-2\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{85}}{2*1}=\frac{-18+2\sqrt{85}}{2}
$