X-12/y=18

Solution for X-12/y=18 equation:

X-12/X=18

We move all terms to the left:

X-12/X-(18)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-18*X-12=0

We add all the numbers together, and all the variables

-18X+X*X-12=0

Wy multiply elements

X^2-18X-12=0

a = 1; b = -18; c = -12;
Δ = b2-4ac
Δ = -182-4·1·(-12)
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*1}=\frac{18-2\sqrt{93}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*1}=\frac{18+2\sqrt{93}}{2}
$