(7+w)-(w+7);w=-4

Solution for (7+w)-(w+7);w=-4 equation:

(7+w)-(w+7)w=-4

We move all terms to the left:

(7+w)-(w+7)w-(-4)=0

We add all the numbers together, and all the variables

(w+7)-(w+7)w-(-4)=0

We add all the numbers together, and all the variables

(w+7)-(w+7)w+4=0

We multiply parentheses

-w^2+(w+7)-7w+4=0

We get rid of parentheses

-w^2+w-7w+7+4=0

We add all the numbers together, and all the variables

-1w^2-6w+11=0

a = -1; b = -6; c = +11;
Δ = b2-4ac
Δ = -62-4·(-1)·11
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{5}}{2*-1}=\frac{6-4\sqrt{5}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{5}}{2*-1}=\frac{6+4\sqrt{5}}{-2}
$