7(24+3w)w=42

Solution for 7(24+3w)w=42 equation:

7(24+3w)w=42

We move all terms to the left:

7(24+3w)w-(42)=0

We add all the numbers together, and all the variables

7(3w+24)w-42=0

We multiply parentheses

21w^2+168w-42=0

a = 21; b = 168; c = -42;
Δ = b2-4ac
Δ = 1682-4·21·(-42)
Δ = 31752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31752}=\sqrt{15876*2}=\sqrt{15876}*\sqrt{2}=126\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-126\sqrt{2}}{2*21}=\frac{-168-126\sqrt{2}}{42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+126\sqrt{2}}{2*21}=\frac{-168+126\sqrt{2}}{42}
$