(2w+3)*w=54

Solution for (2w+3)*w=54 equation:

(2w+3)*w=54

We move all terms to the left:

(2w+3)*w-(54)=0

We multiply parentheses

2w^2+3w-54=0

a = 2; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·2·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*2}=\frac{-24}{4}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*2}=\frac{18}{4}
=4+1/2
$