5/2x+1/6x=8

Solution for 5/2x+1/6x=8 equation:

5/2x+1/6x=8

We move all terms to the left:

5/2x+1/6x-(8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


30x/12x^2+2x/12x^2-8=0

We multiply all the terms by the denominator


30x+2x-8*12x^2=0

We add all the numbers together, and all the variables

32x-8*12x^2=0

Wy multiply elements

-96x^2+32x=0

a = -96; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-96)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-96}=\frac{-64}{-192}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-96}=\frac{0}{-192}
=0
$