2/3y-1/5y+4=19

Solution for 2/3y-1/5y+4=19 equation:

2/3y-1/5y+4=19

We move all terms to the left:

2/3y-1/5y+4-(19)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y-1/5y-15=0

We calculate fractions


10y/15y^2+(-3y)/15y^2-15=0

We multiply all the terms by the denominator


10y+(-3y)-15*15y^2=0

Wy multiply elements

-225y^2+10y+(-3y)=0

We get rid of parentheses

-225y^2+10y-3y=0

We add all the numbers together, and all the variables

-225y^2+7y=0

a = -225; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-225)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-225}=\frac{-14}{-450}
=7/225
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-225}=\frac{0}{-450}
=0
$