6x2-116x+30=0

Solution for 6x2-116x+30=0 equation:

6x^2-116x+30=0

a = 6; b = -116; c = +30;
Δ = b2-4ac
Δ = -1162-4·6·30
Δ = 12736
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:

$\sqrt{\Delta}=\sqrt{12736}=\sqrt{64*199}=\sqrt{64}*\sqrt{199}=8\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-8\sqrt{199}}{2*6}=\frac{116-8\sqrt{199}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+8\sqrt{199}}{2*6}=\frac{116+8\sqrt{199}}{12}
$