12/x=(x-18)/1

Solution for 12/x=(x-18)/1 equation:

12/x=(x-18)/1

We move all terms to the left:

12/x-((x-18)/1)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


()/x^2+(-((x-18)*x)/x^2=0

We multiply all the terms by the denominator


(-((x-18)*x)+()=0


We calculate terms in parentheses: +(-((x-18)*x)+(), so:

-((x-18)*x)+(

We add all the numbers together, and all the variables

-((x-18)*x)


We calculate terms in parentheses: -((x-18)*x), so:

(x-18)*x

We multiply parentheses

x^2-18x

Back to the equation:

-(x^2-18x)


We get rid of parentheses

-x^2+18x

We add all the numbers together, and all the variables

-1x^2+18x

Back to the equation:

+(-1x^2+18x)


We get rid of parentheses

-1x^2+18x=0

a = -1; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-1)·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*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-1}=\frac{0}{-2}
=0
$