(6+f)(6+f)=144

Solution for (6+f)(6+f)=144 equation:

(6+f)(6+f)=144

We move all terms to the left:

(6+f)(6+f)-(144)=0

We add all the numbers together, and all the variables

(f+6)(f+6)-144=0

We multiply parentheses ..

(+f^2+6f+6f+36)-144=0

We get rid of parentheses

f^2+6f+6f+36-144=0

We add all the numbers together, and all the variables

f^2+12f-108=0

a = 1; b = 12; c = -108;
Δ = b2-4ac
Δ = 122-4·1·(-108)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*1}=\frac{-36}{2}
=-18
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*1}=\frac{12}{2}
=6
$