(9x+9)(7x-8)=x

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

(9x+9)(7x-8)=x

We move all terms to the left:

(9x+9)(7x-8)-(x)=0

We add all the numbers together, and all the variables

-1x+(9x+9)(7x-8)=0

We multiply parentheses ..

(+63x^2-72x+63x-72)-1x=0

We get rid of parentheses

63x^2-72x+63x-1x-72=0

We add all the numbers together, and all the variables

63x^2-10x-72=0

a = 63; b = -10; c = -72;
Δ = b2-4ac
Δ = -102-4·63·(-72)
Δ = 18244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18244}=\sqrt{4*4561}=\sqrt{4}*\sqrt{4561}=2\sqrt{4561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{4561}}{2*63}=\frac{10-2\sqrt{4561}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{4561}}{2*63}=\frac{10+2\sqrt{4561}}{126}
$