4w(w+14)+16=0.75

Solution for 4w(w+14)+16=0.75 equation:

4w(w+14)+16=0.75

We move all terms to the left:

4w(w+14)+16-(0.75)=0

We add all the numbers together, and all the variables

4w(w+14)+15.25=0

We multiply parentheses

4w^2+56w+15.25=0

a = 4; b = 56; c = +15.25;
Δ = b2-4ac
Δ = 562-4·4·15.25
Δ = 2892
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{723}}{2*4}=\frac{-56-2\sqrt{723}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{723}}{2*4}=\frac{-56+2\sqrt{723}}{8}
$