(x+2)-7x(7x+14)=0

Solution for (x+2)-7x(7x+14)=0 equation:

(x+2)-7x(7x+14)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-49x^2-97x+2=0

a = -49; b = -97; c = +2;
Δ = b2-4ac
Δ = -972-4·(-49)·2
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-99}{2*-49}=\frac{-2}{-98}
=1/49
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+99}{2*-49}=\frac{196}{-98}
=-2
$