X^2-5x+15=171

Solution for X^2-5x+15=171 equation:

X^2-5X+15=171

We move all terms to the left:

X^2-5X+15-(171)=0

We add all the numbers together, and all the variables

X^2-5X-156=0

a = 1; b = -5; c = -156;
Δ = b2-4ac
Δ = -52-4·1·(-156)
Δ = 649
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{-(-5)-\sqrt{649}}{2*1}=\frac{5-\sqrt{649}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{649}}{2*1}=\frac{5+\sqrt{649}}{2}
$