1/2x-3x=5x

Solution for 1/2x-3x=5x equation:

1/2x-3x=5x

We move all terms to the left:

1/2x-3x-(5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-8x+1/2x=0

We multiply all the terms by the denominator


-8x*2x+1=0

Wy multiply elements

-16x^2+1=0

a = -16; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-16)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-16}=\frac{-8}{-32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-16}=\frac{8}{-32}
=-1/4
$