1/2y+9=1/4y+4

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

1/2y+9=1/4y+4

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y+4)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


4y/8y^2+(-2y)/8y^2-4+9=0

We add all the numbers together, and all the variables

4y/8y^2+(-2y)/8y^2+5=0

We multiply all the terms by the denominator


4y+(-2y)+5*8y^2=0

Wy multiply elements

40y^2+4y+(-2y)=0

We get rid of parentheses

40y^2+4y-2y=0

We add all the numbers together, and all the variables

40y^2+2y=0

a = 40; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·40·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*40}=\frac{-4}{80}
=-1/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*40}=\frac{0}{80}
=0
$