3x2-76x+24=0

Solution for 3x2-76x+24=0 equation:

3x^2-76x+24=0

a = 3; b = -76; c = +24;
Δ = b2-4ac
Δ = -762-4·3·24
Δ = 5488
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:

$\sqrt{\Delta}=\sqrt{5488}=\sqrt{784*7}=\sqrt{784}*\sqrt{7}=28\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-28\sqrt{7}}{2*3}=\frac{76-28\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+28\sqrt{7}}{2*3}=\frac{76+28\sqrt{7}}{6}
$