8/9x+4/2x=1

Solution for 8/9x+4/2x=1 equation:

8/9x+4/2x=1

We move all terms to the left:

8/9x+4/2x-(1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


16x/18x^2+36x/18x^2-1=0

We multiply all the terms by the denominator


16x+36x-1*18x^2=0

We add all the numbers together, and all the variables

52x-1*18x^2=0

Wy multiply elements

-18x^2+52x=0

a = -18; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-18)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-18}=\frac{-104}{-36}
=2+8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-18}=\frac{0}{-36}
=0
$