X^2-9-(7-x)(6-2x)=0

Solution for X^2-9-(7-x)(6-2x)=0 equation:

X^2-9-(7-X)(6-2X)=0

We add all the numbers together, and all the variables

X^2-(-1X+7)(-2X+6)-9=0

We multiply parentheses ..

X^2-(+2X^2-6X-14X+42)-9=0

We get rid of parentheses

X^2-2X^2+6X+14X-42-9=0

We add all the numbers together, and all the variables

-1X^2+20X-51=0

a = -1; b = 20; c = -51;
Δ = b2-4ac
Δ = 202-4·(-1)·(-51)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-14}{2*-1}=\frac{-34}{-2}
=+17
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+14}{2*-1}=\frac{-6}{-2}
=+3
$