3x+5=3/4x

Solution for 3x+5=3/4x equation:

3x+5=3/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-3/4x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2+20x-3=0

a = 12; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·12·(-3)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{34}}{2*12}=\frac{-20-4\sqrt{34}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{34}}{2*12}=\frac{-20+4\sqrt{34}}{24}
$