3x2-84x+24=0

Solution for 3x2-84x+24=0 equation:

3x^2-84x+24=0

a = 3; b = -84; c = +24;
Δ = b2-4ac
Δ = -842-4·3·24
Δ = 6768
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:

$\sqrt{\Delta}=\sqrt{6768}=\sqrt{144*47}=\sqrt{144}*\sqrt{47}=12\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{47}}{2*3}=\frac{84-12\sqrt{47}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{47}}{2*3}=\frac{84+12\sqrt{47}}{6}
$