5/x=(x+1)/4

Solution for 5/x=(x+1)/4 equation:

5/x=(x+1)/4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


(-((x+1)*x)+()=0


We calculate terms in parentheses: +(-((x+1)*x)+(), so:

-((x+1)*x)+(

We add all the numbers together, and all the variables

-((x+1)*x)


We calculate terms in parentheses: -((x+1)*x), so:

(x+1)*x

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x

We add all the numbers together, and all the variables

-1x^2-1x

Back to the equation:

+(-1x^2-1x)


We get rid of parentheses

-1x^2-1x=0

a = -1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-1}=\frac{2}{-2}
=-1
$