20-90x=140-4/x

Solution for 20-90x=140-4/x equation:

20-90x=140-4/x

We move all terms to the left:

20-90x-(140-4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-90x-(-4/x+140)+20=0

We get rid of parentheses

-90x+4/x-140+20=0

We multiply all the terms by the denominator


-90x*x-140*x+20*x+4=0

We add all the numbers together, and all the variables

-120x-90x*x+4=0

Wy multiply elements

-90x^2-120x+4=0

a = -90; b = -120; c = +4;
Δ = b2-4ac
Δ = -1202-4·(-90)·4
Δ = 15840
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:

$\sqrt{\Delta}=\sqrt{15840}=\sqrt{144*110}=\sqrt{144}*\sqrt{110}=12\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-12\sqrt{110}}{2*-90}=\frac{120-12\sqrt{110}}{-180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+12\sqrt{110}}{2*-90}=\frac{120+12\sqrt{110}}{-180}
$