16-u=-4/u=20

Solution for 16-u=-4/u=20 equation:

16-u=-4/u=20

We move all terms to the left:

16-u-(-4/u)=0


Domain of the equation: u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

-1u-(-4/u)+16=0

We get rid of parentheses

-1u+4/u+16=0

We multiply all the terms by the denominator


-1u*u+16*u+4=0

We add all the numbers together, and all the variables

16u-1u*u+4=0

Wy multiply elements

-1u^2+16u+4=0

a = -1; b = 16; c = +4;
Δ = b2-4ac
Δ = 162-4·(-1)·4
Δ = 272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{17}}{2*-1}=\frac{-16-4\sqrt{17}}{-2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{17}}{2*-1}=\frac{-16+4\sqrt{17}}{-2}
$