31+3x(x-71)=180

Solution for 31+3x(x-71)=180 equation:

31+3x(x-71)=180

We move all terms to the left:

31+3x(x-71)-(180)=0

We add all the numbers together, and all the variables

3x(x-71)-149=0

We multiply parentheses

3x^2-213x-149=0

a = 3; b = -213; c = -149;
Δ = b2-4ac
Δ = -2132-4·3·(-149)
Δ = 47157
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{-(-213)-\sqrt{47157}}{2*3}=\frac{213-\sqrt{47157}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-213)+\sqrt{47157}}{2*3}=\frac{213+\sqrt{47157}}{6}
$