36=3w+w^2

Solution for 36=3w+w^2 equation:

36=3w+w^2

We move all terms to the left:

36-(3w+w^2)=0

We get rid of parentheses

-w^2-3w+36=0

We add all the numbers together, and all the variables

-1w^2-3w+36=0

a = -1; b = -3; c = +36;
Δ = b2-4ac
Δ = -32-4·(-1)·36
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*-1}=\frac{3-3\sqrt{17}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*-1}=\frac{3+3\sqrt{17}}{-2}
$