(7-3x)(7-3x)=81

Solution for (7-3x)(7-3x)=81 equation:

(7-3x)(7-3x)=81

We move all terms to the left:

(7-3x)(7-3x)-(81)=0

We add all the numbers together, and all the variables

(-3x+7)(-3x+7)-81=0

We multiply parentheses ..

(+9x^2-21x-21x+49)-81=0

We get rid of parentheses

9x^2-21x-21x+49-81=0

We add all the numbers together, and all the variables

9x^2-42x-32=0

a = 9; b = -42; c = -32;
Δ = b2-4ac
Δ = -422-4·9·(-32)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-54}{2*9}=\frac{-12}{18}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+54}{2*9}=\frac{96}{18}
=5+1/3
$