4x^2+24x-138=0

Solution for 4x^2+24x-138=0 equation:

4x^2+24x-138=0

a = 4; b = 24; c = -138;
Δ = b2-4ac
Δ = 242-4·4·(-138)
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{174}}{2*4}=\frac{-24-4\sqrt{174}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{174}}{2*4}=\frac{-24+4\sqrt{174}}{8}
$