12x^2-9x-8=10x+10

Solution for 12x^2-9x-8=10x+10 equation:

12x^2-9x-8=10x+10

We move all terms to the left:

12x^2-9x-8-(10x+10)=0

We get rid of parentheses

12x^2-9x-10x-10-8=0

We add all the numbers together, and all the variables

12x^2-19x-18=0

a = 12; b = -19; c = -18;
Δ = b2-4ac
Δ = -192-4·12·(-18)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-35}{2*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+35}{2*12}=\frac{54}{24}
=2+1/4
$