4/7x+1/5x=81

Solution for 4/7x+1/5x=81 equation:

4/7x+1/5x=81

We move all terms to the left:

4/7x+1/5x-(81)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


20x/35x^2+7x/35x^2-81=0

We multiply all the terms by the denominator


20x+7x-81*35x^2=0

We add all the numbers together, and all the variables

27x-81*35x^2=0

Wy multiply elements

-2835x^2+27x=0

a = -2835; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-2835)·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*-2835}=\frac{-54}{-5670}
=1/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-2835}=\frac{0}{-5670}
=0
$