3x2-2x=-4x-7x2+12

Solution for 3x2-2x=-4x-7x2+12 equation:

3x^2-2x=-4x-7x^2+12

We move all terms to the left:

3x^2-2x-(-4x-7x^2+12)=0

We get rid of parentheses

3x^2+7x^2+4x-2x-12=0

We add all the numbers together, and all the variables

10x^2+2x-12=0

a = 10; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·10·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*10}=\frac{-24}{20}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*10}=\frac{20}{20}
=1
$