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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/8x^2+(-20x)/8x^2+1-5=0

We add all the numbers together, and all the variables

2x/8x^2+(-20x)/8x^2-4=0

We multiply all the terms by the denominator


2x+(-20x)-4*8x^2=0

Wy multiply elements

-32x^2+2x+(-20x)=0

We get rid of parentheses

-32x^2+2x-20x=0

We add all the numbers together, and all the variables

-32x^2-18x=0

a = -32; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-32)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-32}=\frac{36}{-64}
=-9/16
$