5/9x-14=7/18x-16

Solution for 5/9x-14=7/18x-16 equation:

5/9x-14=7/18x-16

We move all terms to the left:

5/9x-14-(7/18x-16)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 18x-16)!=0

x∈R


We get rid of parentheses

5/9x-7/18x+16-14=0

We calculate fractions


90x/162x^2+(-63x)/162x^2+16-14=0

We add all the numbers together, and all the variables

90x/162x^2+(-63x)/162x^2+2=0

We multiply all the terms by the denominator


90x+(-63x)+2*162x^2=0

Wy multiply elements

324x^2+90x+(-63x)=0

We get rid of parentheses

324x^2+90x-63x=0

We add all the numbers together, and all the variables

324x^2+27x=0

a = 324; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·324·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*324}=\frac{-54}{648}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*324}=\frac{0}{648}
=0
$