-2x2-2x=6x-42

Solution for -2x2-2x=6x-42 equation:

-2x^2-2x=6x-42

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-8x+42=0

a = -2; b = -8; c = +42;
Δ = b2-4ac
Δ = -82-4·(-2)·42
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*-2}=\frac{28}{-4}
=-7
$