(7+w)(7+w)=43

Solution for (7+w)(7+w)=43 equation:

(7+w)(7+w)=43

We move all terms to the left:

(7+w)(7+w)-(43)=0

We add all the numbers together, and all the variables

(w+7)(w+7)-43=0

We multiply parentheses ..

(+w^2+7w+7w+49)-43=0

We get rid of parentheses

w^2+7w+7w+49-43=0

We add all the numbers together, and all the variables

w^2+14w+6=0

a = 1; b = 14; c = +6;
Δ = b2-4ac
Δ = 142-4·1·6
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{43}}{2*1}=\frac{-14-2\sqrt{43}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{43}}{2*1}=\frac{-14+2\sqrt{43}}{2}
$