(x+4)(x-9)=5

Solution for (x+4)(x-9)=5 equation:

(x+4)(x-9)=5

We move all terms to the left:

(x+4)(x-9)-(5)=0

We multiply parentheses ..

(+x^2-9x+4x-36)-5=0

We get rid of parentheses

x^2-9x+4x-36-5=0

We add all the numbers together, and all the variables

x^2-5x-41=0

a = 1; b = -5; c = -41;
Δ = b2-4ac
Δ = -52-4·1·(-41)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{21}}{2*1}=\frac{5-3\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{21}}{2*1}=\frac{5+3\sqrt{21}}{2}
$