(2w-5)w=42

Solution for (2w-5)w=42 equation:

(2w-5)w=42

We move all terms to the left:

(2w-5)w-(42)=0

We multiply parentheses

2w^2-5w-42=0

a = 2; b = -5; c = -42;
Δ = b2-4ac
Δ = -52-4·2·(-42)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*2}=\frac{-14}{4}
=-3+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*2}=\frac{24}{4}
=6
$