3x^2-24x-10=0

Solution for 3x^2-24x-10=0 equation:

3x^2-24x-10=0

a = 3; b = -24; c = -10;
Δ = b2-4ac
Δ = -242-4·3·(-10)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{174}}{2*3}=\frac{24-2\sqrt{174}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{174}}{2*3}=\frac{24+2\sqrt{174}}{6}
$