3/4x+5=1x+3/4x

Solution for 3/4x+5=1x+3/4x equation:

3/4x+5=1x+3/4x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-4x^2+20x=0

a = -4; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-4)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-4}=\frac{0}{-8}
=0
$