2x2=2x+84

Solution for 2x2=2x+84 equation:

2x^2=2x+84

We move all terms to the left:

2x^2-(2x+84)=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{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+26}{2*2}=\frac{28}{4}
=7
$