6y^2=-14y-4

Solution for 6y^2=-14y-4 equation:

6y^2=-14y-4

We move all terms to the left:

6y^2-(-14y-4)=0

We get rid of parentheses

6y^2+14y+4=0

a = 6; b = 14; c = +4;
Δ = b2-4ac
Δ = 142-4·6·4
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*6}=\frac{-24}{12}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*6}=\frac{-4}{12}
=-1/3
$