2x2-9x-65=x2-x

Solution for 2x2-9x-65=x2-x equation:

2x^2-9x-65=x2-x

We move all terms to the left:

2x^2-9x-65-(x2-x)=0

We add all the numbers together, and all the variables

2x^2-(+x^2-1x)-9x-65=0

We get rid of parentheses

2x^2-x^2+1x-9x-65=0

We add all the numbers together, and all the variables

x^2-8x-65=0

a = 1; b = -8; c = -65;
Δ = b2-4ac
Δ = -82-4·1·(-65)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*1}=\frac{26}{2}
=13
$