(2x+3)(x+7)=21721

Solution for (2x+3)(x+7)=21721 equation:

(2x+3)(x+7)=21721

We move all terms to the left:

(2x+3)(x+7)-(21721)=0

We multiply parentheses ..

(+2x^2+14x+3x+21)-21721=0

We get rid of parentheses

2x^2+14x+3x+21-21721=0

We add all the numbers together, and all the variables

2x^2+17x-21700=0

a = 2; b = 17; c = -21700;
Δ = b2-4ac
Δ = 172-4·2·(-21700)
Δ = 173889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173889}=417$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-417}{2*2}=\frac{-434}{4}
=-108+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+417}{2*2}=\frac{400}{4}
=100
$