8(x-9)-9x(x-8)=x+8-(x-6)

Solution for 8(x-9)-9x(x-8)=x+8-(x-6) equation:

8(x-9)-9x(x-8)=x+8-(x-6)

We move all terms to the left:

8(x-9)-9x(x-8)-(x+8-(x-6))=0

We multiply parentheses

-9x^2+8x+72x-(x+8-(x-6))-72=0


We calculate terms in parentheses: -(x+8-(x-6)), so:

x+8-(x-6)

determiningTheFunctionDomain
x-(x-6)+8

We get rid of parentheses

x-x+6+8

We add all the numbers together, and all the variables

14

Back to the equation:

-(14)


We add all the numbers together, and all the variables

-9x^2+80x-86=0

a = -9; b = 80; c = -86;
Δ = b2-4ac
Δ = 802-4·(-9)·(-86)
Δ = 3304
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:

$\sqrt{\Delta}=\sqrt{3304}=\sqrt{4*826}=\sqrt{4}*\sqrt{826}=2\sqrt{826}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{826}}{2*-9}=\frac{-80-2\sqrt{826}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{826}}{2*-9}=\frac{-80+2\sqrt{826}}{-18}
$