3/4x-1=9/5x+4

Solution for 3/4x-1=9/5x+4 equation:

3/4x-1=9/5x+4

We move all terms to the left:

3/4x-1-(9/5x+4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

3/4x-9/5x-4-1=0

We calculate fractions


15x/20x^2+(-36x)/20x^2-4-1=0

We add all the numbers together, and all the variables

15x/20x^2+(-36x)/20x^2-5=0

We multiply all the terms by the denominator


15x+(-36x)-5*20x^2=0

Wy multiply elements

-100x^2+15x+(-36x)=0

We get rid of parentheses

-100x^2+15x-36x=0

We add all the numbers together, and all the variables

-100x^2-21x=0

a = -100; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-100)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-100}=\frac{42}{-200}
=-21/100
$