1/12x+1/19x=1085

Solution for 1/12x+1/19x=1085 equation:

1/12x+1/19x=1085

We move all terms to the left:

1/12x+1/19x-(1085)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 19x!=0

x!=0/19

x!=0

x∈R


We calculate fractions


19x/228x^2+12x/228x^2-1085=0

We multiply all the terms by the denominator


19x+12x-1085*228x^2=0

We add all the numbers together, and all the variables

31x-1085*228x^2=0

Wy multiply elements

-247380x^2+31x=0

a = -247380; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-247380)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-247380}=\frac{-62}{-494760}
=1/7980
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-247380}=\frac{0}{-494760}
=0
$