x^2+8-65=x-5

Solution for x^2+8-65=x-5 equation:

x^2+8-65=x-5

We move all terms to the left:

x^2+8-65-(x-5)=0

We add all the numbers together, and all the variables

x^2-(x-5)-57=0

We get rid of parentheses

x^2-x+5-57=0

We add all the numbers together, and all the variables

x^2-1x-52=0

a = 1; b = -1; c = -52;
Δ = b2-4ac
Δ = -12-4·1·(-52)
Δ = 209
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{-(-1)-\sqrt{209}}{2*1}=\frac{1-\sqrt{209}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{209}}{2*1}=\frac{1+\sqrt{209}}{2}
$