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

Solution for 7(9-x)-8x(9-x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2-7x-72x+63=0

We add all the numbers together, and all the variables

8x^2-79x+63=0

a = 8; b = -79; c = +63;
Δ = b2-4ac
Δ = -792-4·8·63
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-65}{2*8}=\frac{14}{16}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+65}{2*8}=\frac{144}{16}
=9
$