5w(5w+12)=-33

Solution for 5w(5w+12)=-33 equation:

5w(5w+12)=-33

We move all terms to the left:

5w(5w+12)-(-33)=0

We add all the numbers together, and all the variables

5w(5w+12)+33=0

We multiply parentheses

25w^2+60w+33=0

a = 25; b = 60; c = +33;
Δ = b2-4ac
Δ = 602-4·25·33
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-10\sqrt{3}}{2*25}=\frac{-60-10\sqrt{3}}{50}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+10\sqrt{3}}{2*25}=\frac{-60+10\sqrt{3}}{50}
$