(9-x)(6-x)=48.

Solution for (9-x)(6-x)=48. equation:

(9-x)(6-x)=48.

We move all terms to the left:

(9-x)(6-x)-(48.)=0

We add all the numbers together, and all the variables

(-1x+9)(-1x+6)-48=0

We multiply parentheses ..

(+x^2-6x-9x+54)-48=0

We get rid of parentheses

x^2-6x-9x+54-48=0

We add all the numbers together, and all the variables

x^2-15x+6=0

a = 1; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·1·6
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{201}}{2*1}=\frac{15-\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*1}=\frac{15+\sqrt{201}}{2}
$