5/2y-2/3=-7/3y-7

Solution for 5/2y-2/3=-7/3y-7 equation:

5/2y-2/3=-7/3y-7

We move all terms to the left:

5/2y-2/3-(-7/3y-7)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y-7)!=0

y∈R


We get rid of parentheses

5/2y+7/3y+7-2/3=0

We calculate fractions


135y/54y^2+14y/54y^2+(-4y)/54y^2+7=0

We multiply all the terms by the denominator


135y+14y+(-4y)+7*54y^2=0

We add all the numbers together, and all the variables

149y+(-4y)+7*54y^2=0

Wy multiply elements

378y^2+149y+(-4y)=0

We get rid of parentheses

378y^2+149y-4y=0

We add all the numbers together, and all the variables

378y^2+145y=0

a = 378; b = 145; c = 0;
Δ = b2-4ac
Δ = 1452-4·378·0
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(145)-145}{2*378}=\frac{-290}{756}
=-145/378
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(145)+145}{2*378}=\frac{0}{756}
=0
$