w(332532-w)=w/5(33+34)

Solution for w(332532-w)=w/5(33+34) equation:

w(332532-w)=w/5(33+34)

We move all terms to the left:

w(332532-w)-(w/5(33+34))=0

We add all the numbers together, and all the variables

w(-1w+332532)-(w/567)=0

We multiply parentheses

-1w^2+332532w-(w/567)=0

We get rid of parentheses

-1w^2+332532w-w/567=0

We multiply all the terms by the denominator


-1w^2*567+332532w*567-w=0

We add all the numbers together, and all the variables

-1w^2*567-1w+332532w*567=0

Wy multiply elements

-567w^2-1w+188545644w=0

We add all the numbers together, and all the variables

-567w^2+188545643w=0

a = -567; b = 188545643; c = 0;
Δ = b2-4ac
Δ = 1885456432-4·(-567)·0
Δ = 35549459494283449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35549459494283449}=188545643$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(188545643)-188545643}{2*-567}=\frac{-377091286}{-1134}
=332531+566/567
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(188545643)+188545643}{2*-567}=\frac{0}{-1134}
=0
$