11w=33/w+24

Solution for 11w=33/w+24 equation:

11w=33/w+24

We move all terms to the left:

11w-(33/w+24)=0


Domain of the equation: w+24)!=0

w∈R


We get rid of parentheses

11w-33/w-24=0

We multiply all the terms by the denominator


11w*w-24*w-33=0

We add all the numbers together, and all the variables

-24w+11w*w-33=0

Wy multiply elements

11w^2-24w-33=0

a = 11; b = -24; c = -33;
Δ = b2-4ac
Δ = -242-4·11·(-33)
Δ = 2028
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:

$\sqrt{\Delta}=\sqrt{2028}=\sqrt{676*3}=\sqrt{676}*\sqrt{3}=26\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-26\sqrt{3}}{2*11}=\frac{24-26\sqrt{3}}{22}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+26\sqrt{3}}{2*11}=\frac{24+26\sqrt{3}}{22}
$