450=w^2+45w

Solution for 450=w^2+45w equation:

450=w^2+45w

We move all terms to the left:

450-(w^2+45w)=0

We get rid of parentheses

-w^2-45w+450=0

We add all the numbers together, and all the variables

-1w^2-45w+450=0

a = -1; b = -45; c = +450;
Δ = b2-4ac
Δ = -452-4·(-1)·450
Δ = 3825
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:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-15\sqrt{17}}{2*-1}=\frac{45-15\sqrt{17}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15\sqrt{17}}{2*-1}=\frac{45+15\sqrt{17}}{-2}
$