1/16x+1/22X=38

Solution for 1/16x+1/22X=38 equation:

1/16x+1/22x=38

We move all terms to the left:

1/16x+1/22x-(38)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We calculate fractions


22x/352x^2+16x/352x^2-38=0

We multiply all the terms by the denominator


22x+16x-38*352x^2=0

We add all the numbers together, and all the variables

38x-38*352x^2=0

Wy multiply elements

-13376x^2+38x=0

a = -13376; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-13376)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-13376}=\frac{-76}{-26752}
=1/352
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-13376}=\frac{0}{-26752}
=0
$