-2x^2+17=8x-1

Solution for -2x^2+17=8x-1 equation:

-2x^2+17=8x-1

We move all terms to the left:

-2x^2+17-(8x-1)=0

We get rid of parentheses

-2x^2-8x+1+17=0

We add all the numbers together, and all the variables

-2x^2-8x+18=0

a = -2; b = -8; c = +18;
Δ = b2-4ac
Δ = -82-4·(-2)·18
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*-2}=\frac{8-4\sqrt{13}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*-2}=\frac{8+4\sqrt{13}}{-4}
$