X+(40/x)x=90

Solution for X+(40/x)x=90 equation:

X+(40/X)X=90

We move all terms to the left:

X+(40/X)X-(90)=0


Domain of the equation: X)X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+40/X)X-90=0

We multiply parentheses

40X^2+X-90=0

a = 40; b = 1; c = -90;
Δ = b2-4ac
Δ = 12-4·40·(-90)
Δ = 14401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{14401}}{2*40}=\frac{-1-\sqrt{14401}}{80}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{14401}}{2*40}=\frac{-1+\sqrt{14401}}{80}
$