7/10y-2=2/5y+1

Solution for 7/10y-2=2/5y+1 equation:

7/10y-2=2/5y+1

We move all terms to the left:

7/10y-2-(2/5y+1)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R



Domain of the equation: 5y+1)!=0

y∈R


We get rid of parentheses

7/10y-2/5y-1-2=0

We calculate fractions


35y/50y^2+(-20y)/50y^2-1-2=0

We add all the numbers together, and all the variables

35y/50y^2+(-20y)/50y^2-3=0

We multiply all the terms by the denominator


35y+(-20y)-3*50y^2=0

Wy multiply elements

-150y^2+35y+(-20y)=0

We get rid of parentheses

-150y^2+35y-20y=0

We add all the numbers together, and all the variables

-150y^2+15y=0

a = -150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-150)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-150}=\frac{-30}{-300}
=1/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-150}=\frac{0}{-300}
=0
$