(6/x)=(x+7)/(24)

Solution for (6/x)=(x+7)/(24) equation:

(6/x)=(x+7)/(24)

We move all terms to the left:

(6/x)-((x+7)/(24))=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+6/x)-((x+7)/24)=0

We get rid of parentheses

6/x-((x+7)/24)=0

We calculate fractions


()/24x^2+(-((x+7)*x)/24x^2=0

We multiply all the terms by the denominator


(-((x+7)*x)+()=0


We calculate terms in parentheses: +(-((x+7)*x)+(), so:

-((x+7)*x)+(

We add all the numbers together, and all the variables

-((x+7)*x)


We calculate terms in parentheses: -((x+7)*x), so:

(x+7)*x

We multiply parentheses

x^2+7x

Back to the equation:

-(x^2+7x)


We get rid of parentheses

-x^2-7x

We add all the numbers together, and all the variables

-1x^2-7x

Back to the equation:

+(-1x^2-7x)


We get rid of parentheses

-1x^2-7x=0

a = -1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-1)·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*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-1}=\frac{14}{-2}
=-7
$