8y+3+3=y(y+6)

Solution for 8y+3+3=y(y+6) equation:

8y+3+3=y(y+6)

We move all terms to the left:

8y+3+3-(y(y+6))=0

We add all the numbers together, and all the variables

8y-(y(y+6))+6=0


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

y(y+6)

We multiply parentheses

y^2+6y

Back to the equation:

-(y^2+6y)


We get rid of parentheses

-y^2+8y-6y+6=0

We add all the numbers together, and all the variables

-1y^2+2y+6=0

a = -1; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-1)·6
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-1}=\frac{-2-2\sqrt{7}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-1}=\frac{-2+2\sqrt{7}}{-2}
$