5/7y+2=1/2y+3

Solution for 5/7y+2=1/2y+3 equation:

5/7y+2=1/2y+3

We move all terms to the left:

5/7y+2-(1/2y+3)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 2y+3)!=0

y∈R


We get rid of parentheses

5/7y-1/2y-3+2=0

We calculate fractions


10y/14y^2+(-7y)/14y^2-3+2=0

We add all the numbers together, and all the variables

10y/14y^2+(-7y)/14y^2-1=0

We multiply all the terms by the denominator


10y+(-7y)-1*14y^2=0

Wy multiply elements

-14y^2+10y+(-7y)=0

We get rid of parentheses

-14y^2+10y-7y=0

We add all the numbers together, and all the variables

-14y^2+3y=0

a = -14; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-14)·0
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{-(3)-3}{2*-14}=\frac{-6}{-28}
=3/14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-14}=\frac{0}{-28}
=0
$