6/3x+10/5x=256

Solution for 6/3x+10/5x=256 equation:

6/3x+10/5x=256

We move all terms to the left:

6/3x+10/5x-(256)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


30x/15x^2+30x/15x^2-256=0

We multiply all the terms by the denominator


30x+30x-256*15x^2=0

We add all the numbers together, and all the variables

60x-256*15x^2=0

Wy multiply elements

-3840x^2+60x=0

a = -3840; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-3840)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-3840}=\frac{-120}{-7680}
=1/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-3840}=\frac{0}{-7680}
=0
$