4/9x+6/5=5/4x

Solution for 4/9x+6/5=5/4x equation:

4/9x+6/5=5/4x

We move all terms to the left:

4/9x+6/5-(5/4x)=0


Domain of the equation: 9x!=0

x!=0/9

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

4/9x-(+5/4x)+6/5=0

We get rid of parentheses

4/9x-5/4x+6/5=0

We calculate fractions


864x^2/900x^2+400x/900x^2+(-1125x)/900x^2=0

We multiply all the terms by the denominator


864x^2+400x+(-1125x)=0

We get rid of parentheses

864x^2+400x-1125x=0

We add all the numbers together, and all the variables

864x^2-725x=0

a = 864; b = -725; c = 0;
Δ = b2-4ac
Δ = -7252-4·864·0
Δ = 525625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{525625}=725$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-725)-725}{2*864}=\frac{0}{1728}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-725)+725}{2*864}=\frac{1450}{1728}
=725/864
$