9-1/2y=5+4y

Solution for 9-1/2y=5+4y equation:

9-1/2y=5+4y

We move all terms to the left:

9-1/2y-(5+4y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1/2y-(4y+5)+9=0

We get rid of parentheses

-1/2y-4y-5+9=0

We multiply all the terms by the denominator


-4y*2y-5*2y+9*2y-1=0

Wy multiply elements

-8y^2-10y+18y-1=0

We add all the numbers together, and all the variables

-8y^2+8y-1=0

a = -8; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-8)·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*-8}=\frac{-8-4\sqrt{2}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*-8}=\frac{-8+4\sqrt{2}}{-16}
$