X^2+46x-180=0

Solution for X^2+46x-180=0 equation:

X^2+46X-180=0

a = 1; b = 46; c = -180;
Δ = b2-4ac
Δ = 462-4·1·(-180)
Δ = 2836
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:

$\sqrt{\Delta}=\sqrt{2836}=\sqrt{4*709}=\sqrt{4}*\sqrt{709}=2\sqrt{709}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{709}}{2*1}=\frac{-46-2\sqrt{709}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{709}}{2*1}=\frac{-46+2\sqrt{709}}{2}
$