1/2y-1=1/4y+13

Solution for 1/2y-1=1/4y+13 equation:

1/2y-1=1/4y+13

We move all terms to the left:

1/2y-1-(1/4y+13)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y+13)!=0

y∈R


We get rid of parentheses

1/2y-1/4y-13-1=0

We calculate fractions


4y/8y^2+(-2y)/8y^2-13-1=0

We add all the numbers together, and all the variables

4y/8y^2+(-2y)/8y^2-14=0

We multiply all the terms by the denominator


4y+(-2y)-14*8y^2=0

Wy multiply elements

-112y^2+4y+(-2y)=0

We get rid of parentheses

-112y^2+4y-2y=0

We add all the numbers together, and all the variables

-112y^2+2y=0

a = -112; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-112)·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*-112}=\frac{-4}{-224}
=1/56
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-112}=\frac{0}{-224}
=0
$