(X+14)(x-9)=176

Solution for (X+14)(x-9)=176 equation:

(X+14)(X-9)=176

We move all terms to the left:

(X+14)(X-9)-(176)=0

We multiply parentheses ..

(+X^2-9X+14X-126)-176=0

We get rid of parentheses

X^2-9X+14X-126-176=0

We add all the numbers together, and all the variables

X^2+5X-302=0

a = 1; b = 5; c = -302;
Δ = b2-4ac
Δ = 52-4·1·(-302)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{137}}{2*1}=\frac{-5-3\sqrt{137}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{137}}{2*1}=\frac{-5+3\sqrt{137}}{2}
$