3969=(2w+5)*w

Solution for 3969=(2w+5)*w equation:

3969=(2w+5)*w

We move all terms to the left:

3969-((2w+5)*w)=0


We calculate terms in parentheses: -((2w+5)*w), so:

(2w+5)*w

We multiply parentheses

2w^2+5w

Back to the equation:

-(2w^2+5w)


We get rid of parentheses

-2w^2-5w+3969=0

a = -2; b = -5; c = +3969;
Δ = b2-4ac
Δ = -52-4·(-2)·3969
Δ = 31777
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{31777}}{2*-2}=\frac{5-\sqrt{31777}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{31777}}{2*-2}=\frac{5+\sqrt{31777}}{-4}
$