1/12x+1/20x=1

Solution for 1/12x+1/20x=1 equation:

1/12x+1/20x=1

We move all terms to the left:

1/12x+1/20x-(1)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We calculate fractions


20x/240x^2+12x/240x^2-1=0

We multiply all the terms by the denominator


20x+12x-1*240x^2=0

We add all the numbers together, and all the variables

32x-1*240x^2=0

Wy multiply elements

-240x^2+32x=0

a = -240; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-240)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-240}=\frac{-64}{-480}
=2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-240}=\frac{0}{-480}
=0
$