3x2+120=4x2+2x

Solution for 3x2+120=4x2+2x equation:

3x^2+120=4x^2+2x

We move all terms to the left:

3x^2+120-(4x^2+2x)=0

We get rid of parentheses

3x^2-4x^2-2x+120=0

We add all the numbers together, and all the variables

-1x^2-2x+120=0

a = -1; b = -2; c = +120;
Δ = b2-4ac
Δ = -22-4·(-1)·120
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*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*-1}=\frac{24}{-2}
=-12
$