2/5y+3/4y=3

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

2/5y+3/4y=3

We move all terms to the left:

2/5y+3/4y-(3)=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


8y/20y^2+15y/20y^2-3=0

We multiply all the terms by the denominator


8y+15y-3*20y^2=0

We add all the numbers together, and all the variables

23y-3*20y^2=0

Wy multiply elements

-60y^2+23y=0

a = -60; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-60)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-60}=\frac{-46}{-120}
=23/60
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-60}=\frac{0}{-120}
=0
$