12x^2-10x=12x+20

Solution for 12x^2-10x=12x+20 equation:

12x^2-10x=12x+20

We move all terms to the left:

12x^2-10x-(12x+20)=0

We get rid of parentheses

12x^2-10x-12x-20=0

We add all the numbers together, and all the variables

12x^2-22x-20=0

a = 12; b = -22; c = -20;
Δ = b2-4ac
Δ = -222-4·12·(-20)
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*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+38}{2*12}=\frac{60}{24}
=2+1/2
$