6x^2-46x+8=0

Solution for 6x^2-46x+8=0 equation:

6x^2-46x+8=0

a = 6; b = -46; c = +8;
Δ = b2-4ac
Δ = -462-4·6·8
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{481}}{2*6}=\frac{46-2\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{481}}{2*6}=\frac{46+2\sqrt{481}}{12}
$