6(y+1)-4y=y(y+1)

Solution for 6(y+1)-4y=y(y+1) equation:

6(y+1)-4y=y(y+1)

We move all terms to the left:

6(y+1)-4y-(y(y+1))=0

We add all the numbers together, and all the variables

-4y+6(y+1)-(y(y+1))=0

We multiply parentheses

-4y+6y-(y(y+1))+6=0


We calculate terms in parentheses: -(y(y+1)), so:

y(y+1)

We multiply parentheses

y^2+y

Back to the equation:

-(y^2+y)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1y^2+y+6=0

a = -1; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-1)·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-1}=\frac{-6}{-2}
=+3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-1}=\frac{4}{-2}
=-2
$