5w+2w^2=42

Solution for 5w+2w^2=42 equation:

5w+2w^2=42

We move all terms to the left:

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