2x^2-18x+15=8

Solution for 2x^2-18x+15=8 equation:

2x^2-18x+15=8

We move all terms to the left:

2x^2-18x+15-(8)=0

We add all the numbers together, and all the variables

2x^2-18x+7=0

a = 2; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·2·7
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{67}}{2*2}=\frac{18-2\sqrt{67}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{67}}{2*2}=\frac{18+2\sqrt{67}}{4}
$