x^2-13x+20=6

Solution for x^2-13x+20=6 equation:

x^2-13x+20=6

We move all terms to the left:

x^2-13x+20-(6)=0

We add all the numbers together, and all the variables

x^2-13x+14=0

a = 1; b = -13; c = +14;
Δ = b2-4ac
Δ = -132-4·1·14
Δ = 113
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{-(-13)-\sqrt{113}}{2*1}=\frac{13-\sqrt{113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{113}}{2*1}=\frac{13+\sqrt{113}}{2}
$