3x-2/5x=-4x

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

3x-2/5x=-4x

We move all terms to the left:

3x-2/5x-(-4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3x-2/5x+4x=0

We multiply all the terms by the denominator


3x*5x+4x*5x-2=0

Wy multiply elements

15x^2+20x^2-2=0

We add all the numbers together, and all the variables

35x^2-2=0

a = 35; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·35·(-2)
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*35}=\frac{0-2\sqrt{70}}{70}
=-\frac{2\sqrt{70}}{70}
=-\frac{\sqrt{70}}{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*35}=\frac{0+2\sqrt{70}}{70}
=\frac{2\sqrt{70}}{70}
=\frac{\sqrt{70}}{35}
$