(X+9)(x-5)=121

Solution for (X+9)(x-5)=121 equation:

(X+9)(X-5)=121

We move all terms to the left:

(X+9)(X-5)-(121)=0

We multiply parentheses ..

(+X^2-5X+9X-45)-121=0

We get rid of parentheses

X^2-5X+9X-45-121=0

We add all the numbers together, and all the variables

X^2+4X-166=0

a = 1; b = 4; c = -166;
Δ = b2-4ac
Δ = 42-4·1·(-166)
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{170}}{2*1}=\frac{-4-2\sqrt{170}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{170}}{2*1}=\frac{-4+2\sqrt{170}}{2}
$