3(y+2)+4=5(y-1)y

Solution for 3(y+2)+4=5(y-1)y equation:

3(y+2)+4=5(y-1)y

We move all terms to the left:

3(y+2)+4-(5(y-1)y)=0

We multiply parentheses

3y-(5(y-1)y)+6+4=0


We calculate terms in parentheses: -(5(y-1)y), so:

5(y-1)y

We multiply parentheses

5y^2-5y

Back to the equation:

-(5y^2-5y)


We add all the numbers together, and all the variables

3y-(5y^2-5y)+10=0

We get rid of parentheses

-5y^2+3y+5y+10=0

We add all the numbers together, and all the variables

-5y^2+8y+10=0

a = -5; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-5)·10
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{-(8)-2\sqrt{66}}{2*-5}=\frac{-8-2\sqrt{66}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{66}}{2*-5}=\frac{-8+2\sqrt{66}}{-10}
$