0=-3w^2+8w+42

Solution for 0=-3w^2+8w+42 equation:

0=-3w^2+8w+42

We move all terms to the left:

0-(-3w^2+8w+42)=0

We add all the numbers together, and all the variables

-(-3w^2+8w+42)=0

We get rid of parentheses

3w^2-8w-42=0

a = 3; b = -8; c = -42;
Δ = b2-4ac
Δ = -82-4·3·(-42)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{142}}{2*3}=\frac{8-2\sqrt{142}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{142}}{2*3}=\frac{8+2\sqrt{142}}{6}
$