1/23*w=18

Solution for 1/23*w=18 equation:

1/23*w=18

We move all terms to the left:

1/23*w-(18)=0


Domain of the equation: 23*w!=0

w!=0/1

w!=0

w∈R


We multiply all the terms by the denominator


-18*23*w+1=0

Wy multiply elements

-414w*w+1=0

Wy multiply elements

-414w^2+1=0

a = -414; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-414)·1
Δ = 1656
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:

$\sqrt{\Delta}=\sqrt{1656}=\sqrt{36*46}=\sqrt{36}*\sqrt{46}=6\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{46}}{2*-414}=\frac{0-6\sqrt{46}}{-828}
=-\frac{6\sqrt{46}}{-828}
=-\frac{\sqrt{46}}{-138}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{46}}{2*-414}=\frac{0+6\sqrt{46}}{-828}
=\frac{6\sqrt{46}}{-828}
=\frac{\sqrt{46}}{-138}
$