x2-8x-173=0

Solution for x2-8x-173=0 equation:

x2-8x-173=0

We add all the numbers together, and all the variables

x^2-8x-173=0

a = 1; b = -8; c = -173;
Δ = b2-4ac
Δ = -82-4·1·(-173)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{21}}{2*1}=\frac{8-6\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{21}}{2*1}=\frac{8+6\sqrt{21}}{2}
$