1/2y-1/4=2/7y+2

Solution for 1/2y-1/4=2/7y+2 equation:

1/2y-1/4=2/7y+2

We move all terms to the left:

1/2y-1/4-(2/7y+2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 7y+2)!=0

y∈R


We get rid of parentheses

1/2y-2/7y-2-1/4=0

We calculate fractions


(-98y^2)/224y^2+112y/224y^2+(-64y)/224y^2-2=0

We multiply all the terms by the denominator


(-98y^2)+112y+(-64y)-2*224y^2=0

Wy multiply elements

(-98y^2)-448y^2+112y+(-64y)=0

We get rid of parentheses

-98y^2-448y^2+112y-64y=0

We add all the numbers together, and all the variables

-546y^2+48y=0

a = -546; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-546)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-546}=\frac{-96}{-1092}
=8/91
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-546}=\frac{0}{-1092}
=0
$