(2x+1)(2x+3)=19043

Solution for (2x+1)(2x+3)=19043 equation:

(2x+1)(2x+3)=19043

We move all terms to the left:

(2x+1)(2x+3)-(19043)=0

We multiply parentheses ..

(+4x^2+6x+2x+3)-19043=0

We get rid of parentheses

4x^2+6x+2x+3-19043=0

We add all the numbers together, and all the variables

4x^2+8x-19040=0

a = 4; b = 8; c = -19040;
Δ = b2-4ac
Δ = 82-4·4·(-19040)
Δ = 304704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{304704}=552$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-552}{2*4}=\frac{-560}{8}
=-70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+552}{2*4}=\frac{544}{8}
=68
$