(w)(3w-9)=5670

Solution for (w)(3w-9)=5670 equation:

(w)(3w-9)=5670

We move all terms to the left:

(w)(3w-9)-(5670)=0

We multiply parentheses

3w^2-9w-5670=0

a = 3; b = -9; c = -5670;
Δ = b2-4ac
Δ = -92-4·3·(-5670)
Δ = 68121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{68121}=261$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-261}{2*3}=\frac{-252}{6}
=-42
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+261}{2*3}=\frac{270}{6}
=45
$