51+x(x-31)=180

Solution for 51+x(x-31)=180 equation:

51+x(x-31)=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x-31)-129=0

We multiply parentheses

x^2-31x-129=0

a = 1; b = -31; c = -129;
Δ = b2-4ac
Δ = -312-4·1·(-129)
Δ = 1477
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{-(-31)-\sqrt{1477}}{2*1}=\frac{31-\sqrt{1477}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1477}}{2*1}=\frac{31+\sqrt{1477}}{2}
$