53/4w-11=w

Solution for 53/4w-11=w equation:

53/4w-11=w

We move all terms to the left:

53/4w-11-(w)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

-1w+53/4w-11=0

We multiply all the terms by the denominator


-1w*4w-11*4w+53=0

Wy multiply elements

-4w^2-44w+53=0

a = -4; b = -44; c = +53;
Δ = b2-4ac
Δ = -442-4·(-4)·53
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{174}}{2*-4}=\frac{44-4\sqrt{174}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{174}}{2*-4}=\frac{44+4\sqrt{174}}{-8}
$