5x^2-20=180-31x-4

Solution for 5x^2-20=180-31x-4 equation:

5x^2-20=180-31x-4

We move all terms to the left:

5x^2-20-(180-31x-4)=0

We add all the numbers together, and all the variables

5x^2-(-31x+176)-20=0

We get rid of parentheses

5x^2+31x-176-20=0

We add all the numbers together, and all the variables

5x^2+31x-196=0

a = 5; b = 31; c = -196;
Δ = b2-4ac
Δ = 312-4·5·(-196)
Δ = 4881
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{4881}}{2*5}=\frac{-31-\sqrt{4881}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{4881}}{2*5}=\frac{-31+\sqrt{4881}}{10}
$