x-20/x=100

Solution for x-20/x=100 equation:

x-20/x=100

We move all terms to the left:

x-20/x-(100)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-100*x-20=0

We add all the numbers together, and all the variables

-100x+x*x-20=0

Wy multiply elements

x^2-100x-20=0

a = 1; b = -100; c = -20;
Δ = b2-4ac
Δ = -1002-4·1·(-20)
Δ = 10080
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:

$\sqrt{\Delta}=\sqrt{10080}=\sqrt{144*70}=\sqrt{144}*\sqrt{70}=12\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-12\sqrt{70}}{2*1}=\frac{100-12\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+12\sqrt{70}}{2*1}=\frac{100+12\sqrt{70}}{2}
$