x-18/x=90

Solution for x-18/x=90 equation:

x-18/x=90

We move all terms to the left:

x-18/x-(90)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-90*x-18=0

We add all the numbers together, and all the variables

-90x+x*x-18=0

Wy multiply elements

x^2-90x-18=0

a = 1; b = -90; c = -18;
Δ = b2-4ac
Δ = -902-4·1·(-18)
Δ = 8172
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:

$\sqrt{\Delta}=\sqrt{8172}=\sqrt{36*227}=\sqrt{36}*\sqrt{227}=6\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{227}}{2*1}=\frac{90-6\sqrt{227}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{227}}{2*1}=\frac{90+6\sqrt{227}}{2}
$