12x^2-30x+14=0

Solution for 12x^2-30x+14=0 equation:

12x^2-30x+14=0

a = 12; b = -30; c = +14;
Δ = b2-4ac
Δ = -302-4·12·14
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{57}}{2*12}=\frac{30-2\sqrt{57}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{57}}{2*12}=\frac{30+2\sqrt{57}}{24}
$