x(x+12)=85

Solution for x(x+12)=85 equation:

x(x+12)=85

We move all terms to the left:

x(x+12)-(85)=0

We multiply parentheses

x^2+12x-85=0

a = 1; b = 12; c = -85;
Δ = b2-4ac
Δ = 122-4·1·(-85)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-22}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+22}{2*1}=\frac{10}{2}
=5
$