1/4y+10=1/9y.

Solution for 1/4y+10=1/9y. equation:

1/4y+10=1/9y.

We move all terms to the left:

1/4y+10-(1/9y.)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 9y.)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/4y-(+1/9y.)+10=0

We get rid of parentheses

1/4y-1/9y.+10=0

We calculate fractions


9y/36y^2+(-4y)/36y^2+10=0

We multiply all the terms by the denominator


9y+(-4y)+10*36y^2=0

Wy multiply elements

360y^2+9y+(-4y)=0

We get rid of parentheses

360y^2+9y-4y=0

We add all the numbers together, and all the variables

360y^2+5y=0

a = 360; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·360·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*360}=\frac{-10}{720}
=-1/72
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*360}=\frac{0}{720}
=0
$