5x2-20=6x+12

Solution for 5x2-20=6x+12 equation:

5x^2-20=6x+12

We move all terms to the left:

5x^2-20-(6x+12)=0

We get rid of parentheses

5x^2-6x-12-20=0

We add all the numbers together, and all the variables

5x^2-6x-32=0

a = 5; b = -6; c = -32;
Δ = b2-4ac
Δ = -62-4·5·(-32)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-26}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+26}{2*5}=\frac{32}{10}
=3+1/5
$