8x^2-7=77

Solution for 8x^2-7=77 equation:

8x^2-7=77

We move all terms to the left:

8x^2-7-(77)=0

We add all the numbers together, and all the variables

8x^2-84=0

a = 8; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·8·(-84)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{42}}{2*8}=\frac{0-8\sqrt{42}}{16}
=-\frac{8\sqrt{42}}{16}
=-\frac{\sqrt{42}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{42}}{2*8}=\frac{0+8\sqrt{42}}{16}
=\frac{8\sqrt{42}}{16}
=\frac{\sqrt{42}}{2}
$