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

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

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

We move all terms to the left:

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

determiningTheFunctionDomain
2x^2-x^2-9x-65=0

We add all the numbers together, and all the variables

x^2-9x-65=0

a = 1; b = -9; c = -65;
Δ = b2-4ac
Δ = -92-4·1·(-65)
Δ = 341
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{-(-9)-\sqrt{341}}{2*1}=\frac{9-\sqrt{341}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{341}}{2*1}=\frac{9+\sqrt{341}}{2}
$