6y^2+4y-137=0

Solution for 6y^2+4y-137=0 equation:

6y^2+4y-137=0

a = 6; b = 4; c = -137;
Δ = b2-4ac
Δ = 42-4·6·(-137)
Δ = 3304
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:

$\sqrt{\Delta}=\sqrt{3304}=\sqrt{4*826}=\sqrt{4}*\sqrt{826}=2\sqrt{826}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{826}}{2*6}=\frac{-4-2\sqrt{826}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{826}}{2*6}=\frac{-4+2\sqrt{826}}{12}
$