y+6=(y-1)(5y+3)

Solution for y+6=(y-1)(5y+3) equation:

y+6=(y-1)(5y+3)

We move all terms to the left:

y+6-((y-1)(5y+3))=0

We multiply parentheses ..

-((+5y^2+3y-5y-3))+y+6=0


We calculate terms in parentheses: -((+5y^2+3y-5y-3)), so:

(+5y^2+3y-5y-3)

We get rid of parentheses

5y^2+3y-5y-3

We add all the numbers together, and all the variables

5y^2-2y-3

Back to the equation:

-(5y^2-2y-3)


We add all the numbers together, and all the variables

y-(5y^2-2y-3)+6=0

We get rid of parentheses

-5y^2+y+2y+3+6=0

We add all the numbers together, and all the variables

-5y^2+3y+9=0

a = -5; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-5)·9
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*-5}=\frac{-3-3\sqrt{21}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*-5}=\frac{-3+3\sqrt{21}}{-10}
$