3x2-86x+24=0

Solution for 3x2-86x+24=0 equation:

3x^2-86x+24=0

a = 3; b = -86; c = +24;
Δ = b2-4ac
Δ = -862-4·3·24
Δ = 7108
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:

$\sqrt{\Delta}=\sqrt{7108}=\sqrt{4*1777}=\sqrt{4}*\sqrt{1777}=2\sqrt{1777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{1777}}{2*3}=\frac{86-2\sqrt{1777}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{1777}}{2*3}=\frac{86+2\sqrt{1777}}{6}
$