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-x^2)=0

We get rid of parentheses

2x^2+x^2-11x-17=0

We add all the numbers together, and all the variables

3x^2-11x-17=0

a = 3; b = -11; c = -17;
Δ = b2-4ac
Δ = -112-4·3·(-17)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5\sqrt{13}}{2*3}=\frac{11-5\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5\sqrt{13}}{2*3}=\frac{11+5\sqrt{13}}{6}
$