-20x^2-17x+22=12

Solution for -20x^2-17x+22=12 equation:

-20x^2-17x+22=12

We move all terms to the left:

-20x^2-17x+22-(12)=0

We add all the numbers together, and all the variables

-20x^2-17x+10=0

a = -20; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·(-20)·10
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-33}{2*-20}=\frac{-16}{-40}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+33}{2*-20}=\frac{50}{-40}
=-1+1/4
$