(3w-1)(4w+3)=0

Solution for (3w-1)(4w+3)=0 equation:

(3w-1)(4w+3)=0

We multiply parentheses ..

(+12w^2+9w-4w-3)=0

We get rid of parentheses

12w^2+9w-4w-3=0

We add all the numbers together, and all the variables

12w^2+5w-3=0

a = 12; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·12·(-3)
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{-(5)-13}{2*12}=\frac{-18}{24}
=-3/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*12}=\frac{8}{24}
=1/3
$