40=16/x-9.81x

Solution for 40=16/x-9.81x equation:

40=16/x-9.81x

We move all terms to the left:

40-(16/x-9.81x)=0


Domain of the equation: x-9.81x)!=0

x∈R


We add all the numbers together, and all the variables

-(-9.81x+16/x)+40=0

We get rid of parentheses

9.81x-16/x+40=0

We multiply all the terms by the denominator


(9.81x)*x+40*x-16=0

We add all the numbers together, and all the variables

(+9.81x)*x+40*x-16=0

We add all the numbers together, and all the variables

40x+(+9.81x)*x-16=0

We multiply parentheses

9x^2+40x-16=0

a = 9; b = 40; c = -16;
Δ = b2-4ac
Δ = 402-4·9·(-16)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{34}}{2*9}=\frac{-40-8\sqrt{34}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{34}}{2*9}=\frac{-40+8\sqrt{34}}{18}
$