1/16x+1/12x=1

Solution for 1/16x+1/12x=1 equation:

1/16x+1/12x=1

We move all terms to the left:

1/16x+1/12x-(1)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We calculate fractions


12x/192x^2+16x/192x^2-1=0

We multiply all the terms by the denominator


12x+16x-1*192x^2=0

We add all the numbers together, and all the variables

28x-1*192x^2=0

Wy multiply elements

-192x^2+28x=0

a = -192; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-192)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-192}=\frac{-56}{-384}
=7/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-192}=\frac{0}{-384}
=0
$