(5)/(4)y+(3)/(5)y=1

Solution for (5)/(4)y+(3)/(5)y=1 equation:

(5)/(4)y+(3)/(5)y=1

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We calculate fractions


25y/20y^2+12y/20y^2-1=0

We multiply all the terms by the denominator


25y+12y-1*20y^2=0

We add all the numbers together, and all the variables

37y-1*20y^2=0

Wy multiply elements

-20y^2+37y=0

a = -20; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-20)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-20}=\frac{-74}{-40}
=1+17/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-20}=\frac{0}{-40}
=0
$