20x^2-21x-12=x

Solution for 20x^2-21x-12=x equation:

20x^2-21x-12=x

We move all terms to the left:

20x^2-21x-12-(x)=0

We add all the numbers together, and all the variables

20x^2-22x-12=0

a = 20; b = -22; c = -12;
Δ = b2-4ac
Δ = -222-4·20·(-12)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-38}{2*20}=\frac{-16}{40}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+38}{2*20}=\frac{60}{40}
=1+1/2
$