1/2y=4/5y+14

Solution for 1/2y=4/5y+14 equation:

1/2y=4/5y+14

We move all terms to the left:

1/2y-(4/5y+14)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 5y+14)!=0

y∈R


We get rid of parentheses

1/2y-4/5y-14=0

We calculate fractions


5y/10y^2+(-8y)/10y^2-14=0

We multiply all the terms by the denominator


5y+(-8y)-14*10y^2=0

Wy multiply elements

-140y^2+5y+(-8y)=0

We get rid of parentheses

-140y^2+5y-8y=0

We add all the numbers together, and all the variables

-140y^2-3y=0

a = -140; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-140)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-140}=\frac{0}{-280}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-140}=\frac{6}{-280}
=-3/140
$