3/7x+1/5x=66

Solution for 3/7x+1/5x=66 equation:

3/7x+1/5x=66

We move all terms to the left:

3/7x+1/5x-(66)=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


15x/35x^2+7x/35x^2-66=0

We multiply all the terms by the denominator


15x+7x-66*35x^2=0

We add all the numbers together, and all the variables

22x-66*35x^2=0

Wy multiply elements

-2310x^2+22x=0

a = -2310; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-2310)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-2310}=\frac{-44}{-4620}
=1/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-2310}=\frac{0}{-4620}
=0
$