5/4x=7/9x-7

Solution for 5/4x=7/9x-7 equation:

5/4x=7/9x-7

We move all terms to the left:

5/4x-(7/9x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 9x-7)!=0

x∈R


We get rid of parentheses

5/4x-7/9x+7=0

We calculate fractions


45x/36x^2+(-28x)/36x^2+7=0

We multiply all the terms by the denominator


45x+(-28x)+7*36x^2=0

Wy multiply elements

252x^2+45x+(-28x)=0

We get rid of parentheses

252x^2+45x-28x=0

We add all the numbers together, and all the variables

252x^2+17x=0

a = 252; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·252·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*252}=\frac{-34}{504}
=-17/252
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*252}=\frac{0}{504}
=0
$