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-14=0

a = 1; b = -17; c = -14;
Δ = b2-4ac
Δ = -172-4·1·(-14)
Δ = 345
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{345}}{2*1}=\frac{17-\sqrt{345}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{345}}{2*1}=\frac{17+\sqrt{345}}{2}
$