(6-w)(4w-1)=0

Solution for (6-w)(4w-1)=0 equation:

(6-w)(4w-1)=0

We add all the numbers together, and all the variables

(-1w+6)(4w-1)=0

We multiply parentheses ..

(-4w^2+w+24w-6)=0

We get rid of parentheses

-4w^2+w+24w-6=0

We add all the numbers together, and all the variables

-4w^2+25w-6=0

a = -4; b = 25; c = -6;
Δ = b2-4ac
Δ = 252-4·(-4)·(-6)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-23}{2*-4}=\frac{-48}{-8}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+23}{2*-4}=\frac{-2}{-8}
=1/4
$