8x2=68x+220

Solution for 8x2=68x+220 equation:

8x^2=68x+220

We move all terms to the left:

8x^2-(68x+220)=0

We get rid of parentheses

8x^2-68x-220=0

a = 8; b = -68; c = -220;
Δ = b2-4ac
Δ = -682-4·8·(-220)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-108}{2*8}=\frac{-40}{16}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+108}{2*8}=\frac{176}{16}
=11
$