12x2+3x=2-2x

Solution for 12x2+3x=2-2x equation:

12x^2+3x=2-2x

We move all terms to the left:

12x^2+3x-(2-2x)=0

We add all the numbers together, and all the variables

12x^2+3x-(-2x+2)=0

We get rid of parentheses

12x^2+3x+2x-2=0

We add all the numbers together, and all the variables

12x^2+5x-2=0

a = 12; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·12·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*12}=\frac{6}{24}
=1/4
$