3x^2+31=-20x

Solution for 3x^2+31=-20x equation:

3x^2+31=-20x

We move all terms to the left:

3x^2+31-(-20x)=0

We get rid of parentheses

3x^2+20x+31=0

a = 3; b = 20; c = +31;
Δ = b2-4ac
Δ = 202-4·3·31
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{7}}{2*3}=\frac{-20-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{7}}{2*3}=\frac{-20+2\sqrt{7}}{6}
$