84=2x^2-2x

Solution for 84=2x^2-2x equation:

84=2x^2-2x

We move all terms to the left:

84-(2x^2-2x)=0

We get rid of parentheses

-2x^2+2x+84=0

a = -2; b = 2; c = +84;
Δ = b2-4ac
Δ = 22-4·(-2)·84
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-26}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+26}{2*-2}=\frac{24}{-4}
=-6
$