6x^2-30x+12=0

Solution for 6x^2-30x+12=0 equation:

6x^2-30x+12=0

a = 6; b = -30; c = +12;
Δ = b2-4ac
Δ = -302-4·6·12
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{17}}{2*6}=\frac{30-6\sqrt{17}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{17}}{2*6}=\frac{30+6\sqrt{17}}{12}
$