42=(4w+2)(w)

Solution for 42=(4w+2)(w) equation:

42=(4w+2)(w)

We move all terms to the left:

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


We calculate terms in parentheses: -((4w+2)w), so:

(4w+2)w

We multiply parentheses

4w^2+2w

Back to the equation:

-(4w^2+2w)


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
$