X^2-6x-9+(x-3)(x+4)=0

Solution for X^2-6x-9+(x-3)(x+4)=0 equation:

X^2-6X-9+(X-3)(X+4)=0

We multiply parentheses ..

X^2+(+X^2+4X-3X-12)-6X-9=0

We get rid of parentheses

X^2+X^2+4X-3X-6X-12-9=0

We add all the numbers together, and all the variables

2X^2-5X-21=0

a = 2; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·2·(-21)
Δ = 193
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{-(-5)-\sqrt{193}}{2*2}=\frac{5-\sqrt{193}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*2}=\frac{5+\sqrt{193}}{4}
$