(3x+2)/(5x)+(2x-1)/(2x)=4

Solution for (3x+2)/(5x)+(2x-1)/(2x)=4 equation:

(3x+2)/(5x)+(2x-1)/(2x)=4

We move all terms to the left:

(3x+2)/(5x)+(2x-1)/(2x)-(4)=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^2+4x)/10x^2+(10x^2-5x)/10x^2-4=0

We multiply all the terms by the denominator


(6x^2+4x)+(10x^2-5x)-4*10x^2=0

Wy multiply elements

-40x^2+(6x^2+4x)+(10x^2-5x)=0

We get rid of parentheses

-40x^2+6x^2+10x^2+4x-5x=0

We add all the numbers together, and all the variables

-24x^2-1x=0

a = -24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-24)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-24}=\frac{2}{-48}
=-1/24
$