2x^2-4x-65=x^2-12x

Solution for 2x^2-4x-65=x^2-12x equation:

2x^2-4x-65=x^2-12x

We move all terms to the left:

2x^2-4x-65-(x^2-12x)=0

We get rid of parentheses

2x^2-x^2-4x+12x-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{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+18}{2*1}=\frac{10}{2}
=5
$