42w=196+2w^2

Solution for 42w=196+2w^2 equation:

42w=196+2w^2

We move all terms to the left:

42w-(196+2w^2)=0

We get rid of parentheses

-2w^2+42w-196=0

a = -2; b = 42; c = -196;
Δ = b2-4ac
Δ = 422-4·(-2)·(-196)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-14}{2*-2}=\frac{-56}{-4}
=+14
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+14}{2*-2}=\frac{-28}{-4}
=+7
$