8x2=86x+120

Solution for 8x2=86x+120 equation:

8x^2=86x+120

We move all terms to the left:

8x^2-(86x+120)=0

We get rid of parentheses

8x^2-86x-120=0

a = 8; b = -86; c = -120;
Δ = b2-4ac
Δ = -862-4·8·(-120)
Δ = 11236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11236}=106$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-106}{2*8}=\frac{-20}{16}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+106}{2*8}=\frac{192}{16}
=12
$