(4-3x)(4-3x)-9=7

Solution for (4-3x)(4-3x)-9=7 equation:

(4-3x)(4-3x)-9=7

We move all terms to the left:

(4-3x)(4-3x)-9-(7)=0

We add all the numbers together, and all the variables

(-3x+4)(-3x+4)-9-7=0

We add all the numbers together, and all the variables

(-3x+4)(-3x+4)-16=0

We multiply parentheses ..

(+9x^2-12x-12x+16)-16=0

We get rid of parentheses

9x^2-12x-12x+16-16=0

We add all the numbers together, and all the variables

9x^2-24x=0

a = 9; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·9·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*9}=\frac{48}{18}
=2+2/3
$