2x^2+6x=-4x^2+2x+42

Solution for 2x^2+6x=-4x^2+2x+42 equation:

2x^2+6x=-4x^2+2x+42

We move all terms to the left:

2x^2+6x-(-4x^2+2x+42)=0

We get rid of parentheses

2x^2+4x^2-2x+6x-42=0

We add all the numbers together, and all the variables

6x^2+4x-42=0

a = 6; b = 4; c = -42;
Δ = b2-4ac
Δ = 42-4·6·(-42)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-32}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+32}{2*6}=\frac{28}{12}
=2+1/3
$