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

Solution for 4(y+1)+5=6(y-1)y equation:

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

We move all terms to the left:

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

We multiply parentheses

4y-(6(y-1)y)+4+5=0


We calculate terms in parentheses: -(6(y-1)y), so:

6(y-1)y

We multiply parentheses

6y^2-6y

Back to the equation:

-(6y^2-6y)


We add all the numbers together, and all the variables

4y-(6y^2-6y)+9=0

We get rid of parentheses

-6y^2+4y+6y+9=0

We add all the numbers together, and all the variables

-6y^2+10y+9=0

a = -6; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-6)·9
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{79}}{2*-6}=\frac{-10-2\sqrt{79}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{79}}{2*-6}=\frac{-10+2\sqrt{79}}{-12}
$