(x-14)(x+9)=0

Solution for (x-14)(x+9)=0 equation:

(x-14)(x+9)=0

We multiply parentheses ..

(+x^2+9x-14x-126)=0

We get rid of parentheses

x^2+9x-14x-126=0

We add all the numbers together, and all the variables

x^2-5x-126=0

a = 1; b = -5; c = -126;
Δ = b2-4ac
Δ = -52-4·1·(-126)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*1}=\frac{28}{2}
=14
$