x^2+13=8x+37

Solution for x^2+13=8x+37 equation:

x^2+13=8x+37

We move all terms to the left:

x^2+13-(8x+37)=0

We get rid of parentheses

x^2-8x-37+13=0

We add all the numbers together, and all the variables

x^2-8x-24=0

a = 1; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·1·(-24)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*1}=\frac{8-4\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*1}=\frac{8+4\sqrt{10}}{2}
$