(x+7)(14x-7)=0

Solution for (x+7)(14x-7)=0 equation:

(x+7)(14x-7)=0

We multiply parentheses ..

(+14x^2-7x+98x-49)=0

We get rid of parentheses

14x^2-7x+98x-49=0

We add all the numbers together, and all the variables

14x^2+91x-49=0

a = 14; b = 91; c = -49;
Δ = b2-4ac
Δ = 912-4·14·(-49)
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-105}{2*14}=\frac{-196}{28}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+105}{2*14}=\frac{14}{28}
=1/2
$