(x+31)(x+43)=180

Solution for (x+31)(x+43)=180 equation:

(x+31)(x+43)=180

We move all terms to the left:

(x+31)(x+43)-(180)=0

We multiply parentheses ..

(+x^2+43x+31x+1333)-180=0

We get rid of parentheses

x^2+43x+31x+1333-180=0

We add all the numbers together, and all the variables

x^2+74x+1153=0

a = 1; b = 74; c = +1153;
Δ = b2-4ac
Δ = 742-4·1·1153
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-12\sqrt{6}}{2*1}=\frac{-74-12\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+12\sqrt{6}}{2*1}=\frac{-74+12\sqrt{6}}{2}
$