1/2x+8/9x=27

Solution for 1/2x+8/9x=27 equation:

1/2x+8/9x=27

We move all terms to the left:

1/2x+8/9x-(27)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


9x/18x^2+16x/18x^2-27=0

We multiply all the terms by the denominator


9x+16x-27*18x^2=0

We add all the numbers together, and all the variables

25x-27*18x^2=0

Wy multiply elements

-486x^2+25x=0

a = -486; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-486)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-486}=\frac{-50}{-972}
=25/486
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-486}=\frac{0}{-972}
=0
$