5(y+1)-7=3(y-1)2y

Solution for 5(y+1)-7=3(y-1)2y equation:

5(y+1)-7=3(y-1)2y

We move all terms to the left:

5(y+1)-7-(3(y-1)2y)=0

We multiply parentheses

5y-(3(y-1)2y)+5-7=0


We calculate terms in parentheses: -(3(y-1)2y), so:

3(y-1)2y

We multiply parentheses

6y^2-6y

Back to the equation:

-(6y^2-6y)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6y^2+11y-2=0

a = -6; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·(-6)·(-2)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{73}}{2*-6}=\frac{-11-\sqrt{73}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{73}}{2*-6}=\frac{-11+\sqrt{73}}{-12}
$