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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y-2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


(-81y)/108y^2+16y/108y^2+28y/108y^2+2=0

We multiply all the terms by the denominator


(-81y)+16y+28y+2*108y^2=0

We add all the numbers together, and all the variables

44y+(-81y)+2*108y^2=0

Wy multiply elements

216y^2+44y+(-81y)=0

We get rid of parentheses

216y^2+44y-81y=0

We add all the numbers together, and all the variables

216y^2-37y=0

a = 216; b = -37; c = 0;
Δ = b2-4ac
Δ = -372-4·216·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*216}=\frac{0}{432}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*216}=\frac{74}{432}
=37/216
$