(2x+1)+(7x-9)(2x+1)=0

Solution for (2x+1)+(7x-9)(2x+1)=0 equation:

(2x+1)+(7x-9)(2x+1)=0

We get rid of parentheses

2x+(7x-9)(2x+1)+1=0

We multiply parentheses ..

(+14x^2+7x-18x-9)+2x+1=0

We get rid of parentheses

14x^2+7x-18x+2x-9+1=0

We add all the numbers together, and all the variables

14x^2-9x-8=0

a = 14; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·14·(-8)
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{-(-9)-23}{2*14}=\frac{-14}{28}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+23}{2*14}=\frac{32}{28}
=1+1/7
$