14/4x=16/5x+9

Solution for 14/4x=16/5x+9 equation:

14/4x=16/5x+9

We move all terms to the left:

14/4x-(16/5x+9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

14/4x-16/5x-9=0

We calculate fractions


70x/20x^2+(-64x)/20x^2-9=0

We multiply all the terms by the denominator


70x+(-64x)-9*20x^2=0

Wy multiply elements

-180x^2+70x+(-64x)=0

We get rid of parentheses

-180x^2+70x-64x=0

We add all the numbers together, and all the variables

-180x^2+6x=0

a = -180; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-180)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-180}=\frac{-12}{-360}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-180}=\frac{0}{-360}
=0
$