3x2-156x+5=0

Solution for 3x2-156x+5=0 equation:

3x^2-156x+5=0

a = 3; b = -156; c = +5;
Δ = b2-4ac
Δ = -1562-4·3·5
Δ = 24276
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:

$\sqrt{\Delta}=\sqrt{24276}=\sqrt{1156*21}=\sqrt{1156}*\sqrt{21}=34\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-34\sqrt{21}}{2*3}=\frac{156-34\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+34\sqrt{21}}{2*3}=\frac{156+34\sqrt{21}}{6}
$