3x^2-12=5x+20

Solution for 3x^2-12=5x+20 equation:

3x^2-12=5x+20

We move all terms to the left:

3x^2-12-(5x+20)=0

We get rid of parentheses

3x^2-5x-20-12=0

We add all the numbers together, and all the variables

3x^2-5x-32=0

a = 3; b = -5; c = -32;
Δ = b2-4ac
Δ = -52-4·3·(-32)
Δ = 409
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{-(-5)-\sqrt{409}}{2*3}=\frac{5-\sqrt{409}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{409}}{2*3}=\frac{5+\sqrt{409}}{6}
$