(22/w)w+1=42

Solution for (22/w)w+1=42 equation:

(22/w)w+1=42

We move all terms to the left:

(22/w)w+1-(42)=0


Domain of the equation: w)w!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(+22/w)w+1-42=0

We add all the numbers together, and all the variables

(+22/w)w-41=0

We multiply parentheses

22w^2-41=0

a = 22; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·22·(-41)
Δ = 3608
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{902}}{2*22}=\frac{0-2\sqrt{902}}{44}
=-\frac{2\sqrt{902}}{44}
=-\frac{\sqrt{902}}{22}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{902}}{2*22}=\frac{0+2\sqrt{902}}{44}
=\frac{2\sqrt{902}}{44}
=\frac{\sqrt{902}}{22}
$