x^2+13=6x+50

Solution for x^2+13=6x+50 equation:

x^2+13=6x+50

We move all terms to the left:

x^2+13-(6x+50)=0

We get rid of parentheses

x^2-6x-50+13=0

We add all the numbers together, and all the variables

x^2-6x-37=0

a = 1; b = -6; c = -37;
Δ = b2-4ac
Δ = -62-4·1·(-37)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{46}}{2*1}=\frac{6-2\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{46}}{2*1}=\frac{6+2\sqrt{46}}{2}
$