(x-5)(9x-9)=(3x-7)2+8

Solution for (x-5)(9x-9)=(3x-7)2+8 equation:

(x-5)(9x-9)=(3x-7)2+8

We move all terms to the left:

(x-5)(9x-9)-((3x-7)2+8)=0

We multiply parentheses ..

(+9x^2-9x-45x+45)-((3x-7)2+8)=0


We calculate terms in parentheses: -((3x-7)2+8), so:

(3x-7)2+8

We multiply parentheses

6x-14+8

We add all the numbers together, and all the variables

6x-6

Back to the equation:

-(6x-6)


We get rid of parentheses

9x^2-9x-45x-6x+45+6=0

We add all the numbers together, and all the variables

9x^2-60x+51=0

a = 9; b = -60; c = +51;
Δ = b2-4ac
Δ = -602-4·9·51
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-42}{2*9}=\frac{18}{18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+42}{2*9}=\frac{102}{18}
=5+2/3
$