6y^2-21y+12=0

Solution for 6y^2-21y+12=0 equation:

6y^2-21y+12=0

a = 6; b = -21; c = +12;
Δ = b2-4ac
Δ = -212-4·6·12
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{17}}{2*6}=\frac{21-3\sqrt{17}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{17}}{2*6}=\frac{21+3\sqrt{17}}{12}
$