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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

4(y+1)

We multiply parentheses

4y+4

Back to the equation:

-(4y+4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·(-2)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-2}=\frac{-8}{-4}
=+2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-2}=\frac{-2}{-4}
=1/2
$