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

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

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

We move all terms to the left:

-2/3y+3/4y-(4)=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 calculate fractions


(-8y)/12y^2+9y/12y^2-4=0

We multiply all the terms by the denominator


(-8y)+9y-4*12y^2=0

We add all the numbers together, and all the variables

9y+(-8y)-4*12y^2=0

Wy multiply elements

-48y^2+9y+(-8y)=0

We get rid of parentheses

-48y^2+9y-8y=0

We add all the numbers together, and all the variables

-48y^2+y=0

a = -48; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-48)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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