7/5x+3/7x=256

Solution for 7/5x+3/7x=256 equation:

7/5x+3/7x=256

We move all terms to the left:

7/5x+3/7x-(256)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


49x/35x^2+15x/35x^2-256=0

We multiply all the terms by the denominator


49x+15x-256*35x^2=0

We add all the numbers together, and all the variables

64x-256*35x^2=0

Wy multiply elements

-8960x^2+64x=0

a = -8960; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-8960)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-8960}=\frac{-128}{-17920}
=1/140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-8960}=\frac{0}{-17920}
=0
$