18-6-7w-3w(w=12)

Solution for 18-6-7w-3w(w=12) equation:

18-6-7w-3w(w=12)

We move all terms to the left:

18-6-7w-3w(w-(12))=0

We add all the numbers together, and all the variables

-7w-3w(w-12)+12=0

We multiply parentheses

-3w^2-7w+36w+12=0

We add all the numbers together, and all the variables

-3w^2+29w+12=0

a = -3; b = 29; c = +12;
Δ = b2-4ac
Δ = 292-4·(-3)·12
Δ = 985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{985}}{2*-3}=\frac{-29-\sqrt{985}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{985}}{2*-3}=\frac{-29+\sqrt{985}}{-6}
$