2x^2-77=6

Solution for 2x^2-77=6 equation:

2x^2-77=6

We move all terms to the left:

2x^2-77-(6)=0

We add all the numbers together, and all the variables

2x^2-83=0

a = 2; b = 0; c = -83;
Δ = b2-4ac
Δ = 02-4·2·(-83)
Δ = 664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{166}}{2*2}=\frac{0-2\sqrt{166}}{4}
=-\frac{2\sqrt{166}}{4}
=-\frac{\sqrt{166}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{166}}{2*2}=\frac{0+2\sqrt{166}}{4}
=\frac{2\sqrt{166}}{4}
=\frac{\sqrt{166}}{2}
$