3x^2+24x-100=0

Solution for 3x^2+24x-100=0 equation:

3x^2+24x-100=0

a = 3; b = 24; c = -100;
Δ = b2-4ac
Δ = 242-4·3·(-100)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{111}}{2*3}=\frac{-24-4\sqrt{111}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{111}}{2*3}=\frac{-24+4\sqrt{111}}{6}
$