2/7x+1/5x=52

Solution for 2/7x+1/5x=52 equation:

2/7x+1/5x=52

We move all terms to the left:

2/7x+1/5x-(52)=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


10x/35x^2+7x/35x^2-52=0

We multiply all the terms by the denominator


10x+7x-52*35x^2=0

We add all the numbers together, and all the variables

17x-52*35x^2=0

Wy multiply elements

-1820x^2+17x=0

a = -1820; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1820)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-1820}=\frac{-34}{-3640}
=17/1820
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1820}=\frac{0}{-3640}
=0
$