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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


-4x+63x/84x+(-20x)/84x-4=0

We multiply all the terms by the denominator


-4x*84x+63x+(-20x)-4*84x=0

We add all the numbers together, and all the variables

63x-4x*84x+(-20x)-4*84x=0

Wy multiply elements

-336x^2+63x+(-20x)-336x=0

We get rid of parentheses

-336x^2+63x-20x-336x=0

We add all the numbers together, and all the variables

-336x^2-293x=0

a = -336; b = -293; c = 0;
Δ = b2-4ac
Δ = -2932-4·(-336)·0
Δ = 85849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{85849}=293$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-293)-293}{2*-336}=\frac{0}{-672}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-293)+293}{2*-336}=\frac{586}{-672}
=-293/336
$