6(1-4w)w=-18

Solution for 6(1-4w)w=-18 equation:

6(1-4w)w=-18

We move all terms to the left:

6(1-4w)w-(-18)=0

We add all the numbers together, and all the variables

6(-4w+1)w-(-18)=0

We add all the numbers together, and all the variables

6(-4w+1)w+18=0

We multiply parentheses

-24w^2+6w+18=0

a = -24; b = 6; c = +18;
Δ = b2-4ac
Δ = 62-4·(-24)·18
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*-24}=\frac{-48}{-48}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*-24}=\frac{36}{-48}
=-3/4
$