4/15y+5/6y+1/2=8/5

Solution for 4/15y+5/6y+1/2=8/5 equation:

4/15y+5/6y+1/2=8/5

We move all terms to the left:

4/15y+5/6y+1/2-(8/5)=0


Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

4/15y+5/6y+1/2-(+8/5)=0

We get rid of parentheses

4/15y+5/6y+1/2-8/5=0

We calculate fractions


(-8640y^2)/1800y^2+2700y^2/1800y^2+480y/1800y^2+1500y/1800y^2=0

We multiply all the terms by the denominator


(-8640y^2)+2700y^2+480y+1500y=0

We add all the numbers together, and all the variables

2700y^2+(-8640y^2)+1980y=0

We get rid of parentheses

2700y^2-8640y^2+1980y=0

We add all the numbers together, and all the variables

-5940y^2+1980y=0

a = -5940; b = 1980; c = 0;
Δ = b2-4ac
Δ = 19802-4·(-5940)·0
Δ = 3920400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3920400}=1980$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1980)-1980}{2*-5940}=\frac{-3960}{-11880}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1980)+1980}{2*-5940}=\frac{0}{-11880}
=0
$