(X+3)(x-6)=4

Solution for (X+3)(x-6)=4 equation:

(X+3)(X-6)=4

We move all terms to the left:

(X+3)(X-6)-(4)=0

We multiply parentheses ..

(+X^2-6X+3X-18)-4=0

We get rid of parentheses

X^2-6X+3X-18-4=0

We add all the numbers together, and all the variables

X^2-3X-22=0

a = 1; b = -3; c = -22;
Δ = b2-4ac
Δ = -32-4·1·(-22)
Δ = 97
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{-(-3)-\sqrt{97}}{2*1}=\frac{3-\sqrt{97}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{97}}{2*1}=\frac{3+\sqrt{97}}{2}
$