3x^2-28x-24=0

Solution for 3x^2-28x-24=0 equation:

3x^2-28x-24=0

a = 3; b = -28; c = -24;
Δ = b2-4ac
Δ = -282-4·3·(-24)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{67}}{2*3}=\frac{28-4\sqrt{67}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{67}}{2*3}=\frac{28+4\sqrt{67}}{6}
$