42=3w^2-11w

Solution for 42=3w^2-11w equation:

42=3w^2-11w

We move all terms to the left:

42-(3w^2-11w)=0

We get rid of parentheses

-3w^2+11w+42=0

a = -3; b = 11; c = +42;
Δ = b2-4ac
Δ = 112-4·(-3)·42
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*-3}=\frac{-36}{-6}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*-3}=\frac{14}{-6}
=-2+1/3
$