270=(2w-9)(w)

Solution for 270=(2w-9)(w) equation:

270=(2w-9)(w)

We move all terms to the left:

270-((2w-9)(w))=0


We calculate terms in parentheses: -((2w-9)w), so:

(2w-9)w

We multiply parentheses

2w^2-9w

Back to the equation:

-(2w^2-9w)


We get rid of parentheses

-2w^2+9w+270=0

a = -2; b = 9; c = +270;
Δ = b2-4ac
Δ = 92-4·(-2)·270
Δ = 2241
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:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{249}}{2*-2}=\frac{-9-3\sqrt{249}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{249}}{2*-2}=\frac{-9+3\sqrt{249}}{-4}
$