1/x+5-1/4x-7=0

Solution for 1/x+5-1/4x-7=0 equation:

1/x+5-1/4x-7=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We add all the numbers together, and all the variables

4x/4x^2+(-1x)/4x^2-2=0

We multiply all the terms by the denominator


4x+(-1x)-2*4x^2=0

Wy multiply elements

-8x^2+4x+(-1x)=0

We get rid of parentheses

-8x^2+4x-1x=0

We add all the numbers together, and all the variables

-8x^2+3x=0

a = -8; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-8)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-8}=\frac{-6}{-16}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-8}=\frac{0}{-16}
=0
$