5/6x+16=4/9x+9

Solution for 5/6x+16=4/9x+9 equation:

5/6x+16=4/9x+9

We move all terms to the left:

5/6x+16-(4/9x+9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/6x-4/9x-9+16=0

We calculate fractions


45x/54x^2+(-24x)/54x^2-9+16=0

We add all the numbers together, and all the variables

45x/54x^2+(-24x)/54x^2+7=0

We multiply all the terms by the denominator


45x+(-24x)+7*54x^2=0

Wy multiply elements

378x^2+45x+(-24x)=0

We get rid of parentheses

378x^2+45x-24x=0

We add all the numbers together, and all the variables

378x^2+21x=0

a = 378; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·378·0
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*378}=\frac{-42}{756}
=-1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*378}=\frac{0}{756}
=0
$