X^2-17x+59=-2

Solution for X^2-17x+59=-2 equation:

X^2-17X+59=-2

We move all terms to the left:

X^2-17X+59-(-2)=0

We add all the numbers together, and all the variables

X^2-17X+61=0

a = 1; b = -17; c = +61;
Δ = b2-4ac
Δ = -172-4·1·61
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{5}}{2*1}=\frac{17-3\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{5}}{2*1}=\frac{17+3\sqrt{5}}{2}
$