9x+1x/2x=38

Solution for 9x+1x/2x=38 equation:

9x+1x/2x=38

We move all terms to the left:

9x+1x/2x-(38)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x*2x+1x-38*2x=0

We add all the numbers together, and all the variables

x+9x*2x-38*2x=0

Wy multiply elements

18x^2+x-76x=0

We add all the numbers together, and all the variables

18x^2-75x=0

a = 18; b = -75; c = 0;
Δ = b2-4ac
Δ = -752-4·18·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-75}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+75}{2*18}=\frac{150}{36}
=4+1/6
$