2/5x+3/2x=3

Solution for 2/5x+3/2x=3 equation:

2/5x+3/2x=3

We move all terms to the left:

2/5x+3/2x-(3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


4x/10x^2+15x/10x^2-3=0

We multiply all the terms by the denominator


4x+15x-3*10x^2=0

We add all the numbers together, and all the variables

19x-3*10x^2=0

Wy multiply elements

-30x^2+19x=0

a = -30; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-30)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-30}=\frac{-38}{-60}
=19/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-30}=\frac{0}{-60}
=0
$