(2x+3)+(2x+3)(7x-2)=0

Solution for (2x+3)+(2x+3)(7x-2)=0 equation:

(2x+3)+(2x+3)(7x-2)=0

We get rid of parentheses

2x+(2x+3)(7x-2)+3=0

We multiply parentheses ..

(+14x^2-4x+21x-6)+2x+3=0

We get rid of parentheses

14x^2-4x+21x+2x-6+3=0

We add all the numbers together, and all the variables

14x^2+19x-3=0

a = 14; b = 19; c = -3;
Δ = b2-4ac
Δ = 192-4·14·(-3)
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{-(19)-23}{2*14}=\frac{-42}{28}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*14}=\frac{4}{28}
=1/7
$