(X+5)(x-9)=21

Solution for (X+5)(x-9)=21 equation:

(X+5)(X-9)=21

We move all terms to the left:

(X+5)(X-9)-(21)=0

We multiply parentheses ..

(+X^2-9X+5X-45)-21=0

We get rid of parentheses

X^2-9X+5X-45-21=0

We add all the numbers together, and all the variables

X^2-4X-66=0

a = 1; b = -4; c = -66;
Δ = b2-4ac
Δ = -42-4·1·(-66)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{70}}{2*1}=\frac{4-2\sqrt{70}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{70}}{2*1}=\frac{4+2\sqrt{70}}{2}
$