3x/4x+5=4x-4/21

Solution for 3x/4x+5=4x-4/21 equation:

3x/4x+5=4x-4/21

We move all terms to the left:

3x/4x+5-(4x-4/21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x/4x-(+4x-4/21)+5=0

We get rid of parentheses

3x/4x-4x+5+4/21=0

We calculate fractions


-4x+63x/84x+16x/84x+5=0

We multiply all the terms by the denominator


-4x*84x+63x+16x+5*84x=0

We add all the numbers together, and all the variables

79x-4x*84x+5*84x=0

Wy multiply elements

-336x^2+79x+420x=0

We add all the numbers together, and all the variables

-336x^2+499x=0

a = -336; b = 499; c = 0;
Δ = b2-4ac
Δ = 4992-4·(-336)·0
Δ = 249001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{249001}=499$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(499)-499}{2*-336}=\frac{-998}{-672}
=1+163/336
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(499)+499}{2*-336}=\frac{0}{-672}
=0
$