X^2-14x-180=0

Solution for X^2-14x-180=0 equation:

X^2-14X-180=0

a = 1; b = -14; c = -180;
Δ = b2-4ac
Δ = -142-4·1·(-180)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{229}}{2*1}=\frac{14-2\sqrt{229}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{229}}{2*1}=\frac{14+2\sqrt{229}}{2}
$