6x^2-48x+3=0

Solution for 6x^2-48x+3=0 equation:

6x^2-48x+3=0

a = 6; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·6·3
Δ = 2232
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:

$\sqrt{\Delta}=\sqrt{2232}=\sqrt{36*62}=\sqrt{36}*\sqrt{62}=6\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{62}}{2*6}=\frac{48-6\sqrt{62}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{62}}{2*6}=\frac{48+6\sqrt{62}}{12}
$