3/5y+2=3/4y+7

Solution for 3/5y+2=3/4y+7 equation:

3/5y+2=3/4y+7

We move all terms to the left:

3/5y+2-(3/4y+7)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y+7)!=0

y∈R


We get rid of parentheses

3/5y-3/4y-7+2=0

We calculate fractions


12y/20y^2+(-15y)/20y^2-7+2=0

We add all the numbers together, and all the variables

12y/20y^2+(-15y)/20y^2-5=0

We multiply all the terms by the denominator


12y+(-15y)-5*20y^2=0

Wy multiply elements

-100y^2+12y+(-15y)=0

We get rid of parentheses

-100y^2+12y-15y=0

We add all the numbers together, and all the variables

-100y^2-3y=0

a = -100; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-100)·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*-100}=\frac{0}{-200}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-100}=\frac{6}{-200}
=-3/100
$