6y2=-8y-1

Solution for 6y2=-8y-1 equation:

6y^2=-8y-1

We move all terms to the left:

6y^2-(-8y-1)=0

We get rid of parentheses

6y^2+8y+1=0

a = 6; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·6·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{10}}{2*6}=\frac{-8-2\sqrt{10}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{10}}{2*6}=\frac{-8+2\sqrt{10}}{12}
$