3x^2-102x+312=0

Solution for 3x^2-102x+312=0 equation:

3x^2-102x+312=0

a = 3; b = -102; c = +312;
Δ = b2-4ac
Δ = -1022-4·3·312
Δ = 6660
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:

$\sqrt{\Delta}=\sqrt{6660}=\sqrt{36*185}=\sqrt{36}*\sqrt{185}=6\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{185}}{2*3}=\frac{102-6\sqrt{185}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{185}}{2*3}=\frac{102+6\sqrt{185}}{6}
$