0=4w^2+2w-42

Solution for 0=4w^2+2w-42 equation:

0=4w^2+2w-42

We move all terms to the left:

0-(4w^2+2w-42)=0

We add all the numbers together, and all the variables

-(4w^2+2w-42)=0

We get rid of parentheses

-4w^2-2w+42=0

a = -4; b = -2; c = +42;
Δ = b2-4ac
Δ = -22-4·(-4)·42
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-26}{2*-4}=\frac{-24}{-8}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+26}{2*-4}=\frac{28}{-8}
=-3+1/2
$