1/5y+1/4y=10

Solution for 1/5y+1/4y=10 equation:

1/5y+1/4y=10

We move all terms to the left:

1/5y+1/4y-(10)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


4y/20y^2+5y/20y^2-10=0

We multiply all the terms by the denominator


4y+5y-10*20y^2=0

We add all the numbers together, and all the variables

9y-10*20y^2=0

Wy multiply elements

-200y^2+9y=0

a = -200; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-200)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-200}=\frac{-18}{-400}
=9/200
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-200}=\frac{0}{-400}
=0
$