(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

(-1w+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+27w-18=0

a = -4; b = 27; c = -18;
Δ = b2-4ac
Δ = 272-4·(-4)·(-18)
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{-(27)-21}{2*-4}=\frac{-48}{-8}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+21}{2*-4}=\frac{-6}{-8}
=3/4
$