6(y+1)-9=4(y-1)2y

Solution for 6(y+1)-9=4(y-1)2y equation:

6(y+1)-9=4(y-1)2y

We move all terms to the left:

6(y+1)-9-(4(y-1)2y)=0

We multiply parentheses

6y-(4(y-1)2y)+6-9=0


We calculate terms in parentheses: -(4(y-1)2y), so:

4(y-1)2y

We multiply parentheses

8y^2-8y

Back to the equation:

-(8y^2-8y)


We add all the numbers together, and all the variables

6y-(8y^2-8y)-3=0

We get rid of parentheses

-8y^2+6y+8y-3=0

We add all the numbers together, and all the variables

-8y^2+14y-3=0

a = -8; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-8)·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-8}=\frac{-4}{-16}
=1/4
$