2x^2-11x=17=x^2

Solution for 2x^2-11x=17=x^2 equation:

2x^2-11x=17=x^2

We move all terms to the left:

2x^2-11x-(17)=0

a = 2; b = -11; c = -17;
Δ = b2-4ac
Δ = -112-4·2·(-17)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{257}}{2*2}=\frac{11-\sqrt{257}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{257}}{2*2}=\frac{11+\sqrt{257}}{4}
$