x^2-17x+13=24

Solution for x^2-17x+13=24 equation:

x^2-17x+13=24

We move all terms to the left:

x^2-17x+13-(24)=0

We add all the numbers together, and all the variables

x^2-17x-11=0

a = 1; b = -17; c = -11;
Δ = b2-4ac
Δ = -172-4·1·(-11)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{37}}{2*1}=\frac{17-3\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{37}}{2*1}=\frac{17+3\sqrt{37}}{2}
$