(2w-7)(w+3)=0

Solution for (2w-7)(w+3)=0 equation:

(2w-7)(w+3)=0

We multiply parentheses ..

(+2w^2+6w-7w-21)=0

We get rid of parentheses

2w^2+6w-7w-21=0

We add all the numbers together, and all the variables

2w^2-1w-21=0

a = 2; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·2·(-21)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*2}=\frac{-12}{4}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*2}=\frac{14}{4}
=3+1/2
$