X^2+24x-190=0

Solution for X^2+24x-190=0 equation:

X^2+24X-190=0

a = 1; b = 24; c = -190;
Δ = b2-4ac
Δ = 242-4·1·(-190)
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{334}}{2*1}=\frac{-24-2\sqrt{334}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{334}}{2*1}=\frac{-24+2\sqrt{334}}{2}
$