X^2-6x-65=7

Solution for X^2-6x-65=7 equation:

X^2-6X-65=7

We move all terms to the left:

X^2-6X-65-(7)=0

We add all the numbers together, and all the variables

X^2-6X-72=0

a = 1; b = -6; c = -72;
Δ = b2-4ac
Δ = -62-4·1·(-72)
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{-(-6)-18}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*1}=\frac{24}{2}
=12
$