13x^2+91x-9=x

Solution for 13x^2+91x-9=x equation:

13x^2+91x-9=x

We move all terms to the left:

13x^2+91x-9-(x)=0

We add all the numbers together, and all the variables

13x^2+90x-9=0

a = 13; b = 90; c = -9;
Δ = b2-4ac
Δ = 902-4·13·(-9)
Δ = 8568
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:

$\sqrt{\Delta}=\sqrt{8568}=\sqrt{36*238}=\sqrt{36}*\sqrt{238}=6\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{238}}{2*13}=\frac{-90-6\sqrt{238}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{238}}{2*13}=\frac{-90+6\sqrt{238}}{26}
$