(4+w)(w)=75

Solution for (4+w)(w)=75 equation:

(4+w)(w)=75

We move all terms to the left:

(4+w)(w)-(75)=0

We add all the numbers together, and all the variables

(w+4)w-75=0

We multiply parentheses

w^2+4w-75=0

a = 1; b = 4; c = -75;
Δ = b2-4ac
Δ = 42-4·1·(-75)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{79}}{2*1}=\frac{-4-2\sqrt{79}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{79}}{2*1}=\frac{-4+2\sqrt{79}}{2}
$