7x^2-8x=8

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

7x^2-8x=8

We move all terms to the left:

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

a = 7; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·7·(-8)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{2}}{2*7}=\frac{8-12\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{2}}{2*7}=\frac{8+12\sqrt{2}}{14}
$