(X+8)(x+8)-3(x+3)=185

Solution for (X+8)(x+8)-3(x+3)=185 equation:

(X+8)(X+8)-3(X+3)=185

We move all terms to the left:

(X+8)(X+8)-3(X+3)-(185)=0

We multiply parentheses

(X+8)(X+8)-3X-9-185=0

We multiply parentheses ..

(+X^2+8X+8X+64)-3X-9-185=0

We add all the numbers together, and all the variables

(+X^2+8X+8X+64)-3X-194=0

We get rid of parentheses

X^2+8X+8X-3X+64-194=0

We add all the numbers together, and all the variables

X^2+13X-130=0

a = 1; b = 13; c = -130;
Δ = b2-4ac
Δ = 132-4·1·(-130)
Δ = 689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{689}}{2*1}=\frac{-13-\sqrt{689}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{689}}{2*1}=\frac{-13+\sqrt{689}}{2}
$