(5-x)(3+x)=9

Solution for (5-x)(3+x)=9 equation:

(5-x)(3+x)=9

We move all terms to the left:

(5-x)(3+x)-(9)=0

We add all the numbers together, and all the variables

(-1x+5)(x+3)-9=0

We multiply parentheses ..

(-1x^2-3x+5x+15)-9=0

We get rid of parentheses

-1x^2-3x+5x+15-9=0

We add all the numbers together, and all the variables

-1x^2+2x+6=0

a = -1; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-1)·6
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-1}=\frac{-2-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-1}=\frac{-2+2\sqrt{7}}{-2}
$