(5w+1)w=48

Solution for (5w+1)w=48 equation:

(5w+1)w=48

We move all terms to the left:

(5w+1)w-(48)=0

We multiply parentheses

5w^2+w-48=0

a = 5; b = 1; c = -48;
Δ = b2-4ac
Δ = 12-4·5·(-48)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*5}=\frac{-32}{10}
=-3+1/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*5}=\frac{30}{10}
=3
$