x^2-17x+13=-27

Solution for x^2-17x+13=-27 equation:

x^2-17x+13=-27

We move all terms to the left:

x^2-17x+13-(-27)=0

We add all the numbers together, and all the variables

x^2-17x+40=0

a = 1; b = -17; c = +40;
Δ = b2-4ac
Δ = -172-4·1·40
Δ = 129
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{-(-17)-\sqrt{129}}{2*1}=\frac{17-\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{129}}{2*1}=\frac{17+\sqrt{129}}{2}
$