5/4y-3=7/6y

Solution for 5/4y-3=7/6y equation:

5/4y-3=7/6y

We move all terms to the left:

5/4y-3-(7/6y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

5/4y-(+7/6y)-3=0

We get rid of parentheses

5/4y-7/6y-3=0

We calculate fractions


30y/24y^2+(-28y)/24y^2-3=0

We multiply all the terms by the denominator


30y+(-28y)-3*24y^2=0

Wy multiply elements

-72y^2+30y+(-28y)=0

We get rid of parentheses

-72y^2+30y-28y=0

We add all the numbers together, and all the variables

-72y^2+2y=0

a = -72; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-72)·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*-72}=\frac{-4}{-144}
=1/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-72}=\frac{0}{-144}
=0
$