(7+w)-(w+7);w=-9

Solution for (7+w)-(w+7);w=-9 equation:

(7+w)-(w+7)w=-9

We move all terms to the left:

(7+w)-(w+7)w-(-9)=0

We add all the numbers together, and all the variables

(w+7)-(w+7)w-(-9)=0

We add all the numbers together, and all the variables

(w+7)-(w+7)w+9=0

We multiply parentheses

-w^2+(w+7)-7w+9=0

We get rid of parentheses

-w^2+w-7w+7+9=0

We add all the numbers together, and all the variables

-1w^2-6w+16=0

a = -1; b = -6; c = +16;
Δ = b2-4ac
Δ = -62-4·(-1)·16
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-1}=\frac{-4}{-2}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-1}=\frac{16}{-2}
=-8
$