Y-1/2y=7-4/3y

Solution for Y-1/2y=7-4/3y equation:

-1/2Y=7-4/3Y

We move all terms to the left:

-1/2Y-(7-4/3Y)=0


Domain of the equation: 2Y!=0

Y!=0/2

Y!=0

Y∈R



Domain of the equation: 3Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

-1/2Y-(-4/3Y+7)=0

We get rid of parentheses

-1/2Y+4/3Y-7=0

We calculate fractions


(-3Y)/6Y^2+8Y/6Y^2-7=0

We multiply all the terms by the denominator


(-3Y)+8Y-7*6Y^2=0

We add all the numbers together, and all the variables

8Y+(-3Y)-7*6Y^2=0

Wy multiply elements

-42Y^2+8Y+(-3Y)=0

We get rid of parentheses

-42Y^2+8Y-3Y=0

We add all the numbers together, and all the variables

-42Y^2+5Y=0

a = -42; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-42)·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*-42}=\frac{-10}{-84}
=5/42
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-42}=\frac{0}{-84}
=0
$