1/11x+1/16x=1

Solution for 1/11x+1/16x=1 equation:

1/11x+1/16x=1

We move all terms to the left:

1/11x+1/16x-(1)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R


We calculate fractions


16x/176x^2+11x/176x^2-1=0

We multiply all the terms by the denominator


16x+11x-1*176x^2=0

We add all the numbers together, and all the variables

27x-1*176x^2=0

Wy multiply elements

-176x^2+27x=0

a = -176; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-176)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-176}=\frac{-54}{-352}
=27/176
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-176}=\frac{0}{-352}
=0
$