2/3y-1/4y=-1

Solution for 2/3y-1/4y=-1 equation:

2/3y-1/4y=-1

We move all terms to the left:

2/3y-1/4y-(-1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y-1/4y+1=0

We calculate fractions


8y/12y^2+(-3y)/12y^2+1=0

We multiply all the terms by the denominator


8y+(-3y)+1*12y^2=0

Wy multiply elements

12y^2+8y+(-3y)=0

We get rid of parentheses

12y^2+8y-3y=0

We add all the numbers together, and all the variables

12y^2+5y=0

a = 12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*12}=\frac{-10}{24}
=-5/12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*12}=\frac{0}{24}
=0
$