(x-14)(x+17)=0

Solution for (x-14)(x+17)=0 equation:

(x-14)(x+17)=0

We multiply parentheses ..

(+x^2+17x-14x-238)=0

We get rid of parentheses

x^2+17x-14x-238=0

We add all the numbers together, and all the variables

x^2+3x-238=0

a = 1; b = 3; c = -238;
Δ = b2-4ac
Δ = 32-4·1·(-238)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-31}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+31}{2*1}=\frac{28}{2}
=14
$