(2x-1)(x+14)=0

Solution for (2x-1)(x+14)=0 equation:

(2x-1)(x+14)=0

We multiply parentheses ..

(+2x^2+28x-1x-14)=0

We get rid of parentheses

2x^2+28x-1x-14=0

We add all the numbers together, and all the variables

2x^2+27x-14=0

a = 2; b = 27; c = -14;
Δ = b2-4ac
Δ = 272-4·2·(-14)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-29}{2*2}=\frac{-56}{4}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+29}{2*2}=\frac{2}{4}
=1/2
$