75=w(3w+2)

Solution for 75=w(3w+2) equation:

75=w(3w+2)

We move all terms to the left:

75-(w(3w+2))=0


We calculate terms in parentheses: -(w(3w+2)), so:

w(3w+2)

We multiply parentheses

3w^2+2w

Back to the equation:

-(3w^2+2w)


We get rid of parentheses

-3w^2-2w+75=0

a = -3; b = -2; c = +75;
Δ = b2-4ac
Δ = -22-4·(-3)·75
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{226}}{2*-3}=\frac{2-2\sqrt{226}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{226}}{2*-3}=\frac{2+2\sqrt{226}}{-6}
$