5=6y(y+2)=5y+8

Solution for 5=6y(y+2)=5y+8 equation:

5=6y(y+2)=5y+8

We move all terms to the left:

5-(6y(y+2))=0


We calculate terms in parentheses: -(6y(y+2)), so:

6y(y+2)

We multiply parentheses

6y^2+12y

Back to the equation:

-(6y^2+12y)


We get rid of parentheses

-6y^2-12y+5=0

a = -6; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·(-6)·5
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*-6}=\frac{12-2\sqrt{66}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*-6}=\frac{12+2\sqrt{66}}{-12}
$