6y2-86y+21=0

Solution for 6y2-86y+21=0 equation:

6y^2-86y+21=0

a = 6; b = -86; c = +21;
Δ = b2-4ac
Δ = -862-4·6·21
Δ = 6892
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:

$\sqrt{\Delta}=\sqrt{6892}=\sqrt{4*1723}=\sqrt{4}*\sqrt{1723}=2\sqrt{1723}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{1723}}{2*6}=\frac{86-2\sqrt{1723}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{1723}}{2*6}=\frac{86+2\sqrt{1723}}{12}
$