(2w-3)(6+w)=0

Solution for (2w-3)(6+w)=0 equation:

(2w-3)(6+w)=0

We add all the numbers together, and all the variables

(2w-3)(w+6)=0

We multiply parentheses ..

(+2w^2+12w-3w-18)=0

We get rid of parentheses

2w^2+12w-3w-18=0

We add all the numbers together, and all the variables

2w^2+9w-18=0

a = 2; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·2·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*2}=\frac{-24}{4}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*2}=\frac{6}{4}
=1+1/2
$