6y^2+18y-4=0

Solution for 6y^2+18y-4=0 equation:

6y^2+18y-4=0

a = 6; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·6·(-4)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*6}=\frac{-18-2\sqrt{105}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*6}=\frac{-18+2\sqrt{105}}{12}
$