3/5x-4/2x=3

Solution for 3/5x-4/2x=3 equation:

3/5x-4/2x=3

We move all terms to the left:

3/5x-4/2x-(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


6x/10x^2+(-20x)/10x^2-3=0

We multiply all the terms by the denominator


6x+(-20x)-3*10x^2=0

Wy multiply elements

-30x^2+6x+(-20x)=0

We get rid of parentheses

-30x^2+6x-20x=0

We add all the numbers together, and all the variables

-30x^2-14x=0

a = -30; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-30)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-30}=\frac{28}{-60}
=-7/15
$