7/10y+3/2=3/5y+2

Solution for 7/10y+3/2=3/5y+2 equation:

7/10y+3/2=3/5y+2

We move all terms to the left:

7/10y+3/2-(3/5y+2)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 5y+2)!=0

y∈R


We get rid of parentheses

7/10y-3/5y-2+3/2=0

We calculate fractions


750y^2/200y^2+140y/200y^2+(-120y)/200y^2-2=0

We multiply all the terms by the denominator


750y^2+140y+(-120y)-2*200y^2=0

Wy multiply elements

750y^2-400y^2+140y+(-120y)=0

We get rid of parentheses

750y^2-400y^2+140y-120y=0

We add all the numbers together, and all the variables

350y^2+20y=0

a = 350; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·350·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*350}=\frac{-40}{700}
=-2/35
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*350}=\frac{0}{700}
=0
$