(X+4)(x-9)=68

Solution for (X+4)(x-9)=68 equation:

(X+4)(X-9)=68

We move all terms to the left:

(X+4)(X-9)-(68)=0

We multiply parentheses ..

(+X^2-9X+4X-36)-68=0

We get rid of parentheses

X^2-9X+4X-36-68=0

We add all the numbers together, and all the variables

X^2-5X-104=0

a = 1; b = -5; c = -104;
Δ = b2-4ac
Δ = -52-4·1·(-104)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-21}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+21}{2*1}=\frac{26}{2}
=13
$