x/2x-5=4x-1

Solution for x/2x-5=4x-1 equation:

x/2x-5=4x-1

We move all terms to the left:

x/2x-5-(4x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x/2x-4x+1-5=0

We multiply all the terms by the denominator


x-4x*2x+1*2x-5*2x=0

Wy multiply elements

-8x^2+x+2x-10x=0

We add all the numbers together, and all the variables

-8x^2-7x=0

a = -8; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-8)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-8}=\frac{14}{-16}
=-7/8
$