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

Solution for (6+w)(4w-3)=0 equation:

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

We add all the numbers together, and all the variables

(w+6)(4w-3)=0

We multiply parentheses ..

(+4w^2-3w+24w-18)=0

We get rid of parentheses

4w^2-3w+24w-18=0

We add all the numbers together, and all the variables

4w^2+21w-18=0

a = 4; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·4·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*4}=\frac{-48}{8}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*4}=\frac{6}{8}
=3/4
$