x^2+24x-172=0

Solution for x^2+24x-172=0 equation:

x^2+24x-172=0

a = 1; b = 24; c = -172;
Δ = b2-4ac
Δ = 242-4·1·(-172)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{79}}{2*1}=\frac{-24-4\sqrt{79}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{79}}{2*1}=\frac{-24+4\sqrt{79}}{2}
$