(x+7)(2x+19)=83

Solution for (x+7)(2x+19)=83 equation:

(x+7)(2x+19)=83

We move all terms to the left:

(x+7)(2x+19)-(83)=0

We multiply parentheses ..

(+2x^2+19x+14x+133)-83=0

We get rid of parentheses

2x^2+19x+14x+133-83=0

We add all the numbers together, and all the variables

2x^2+33x+50=0

a = 2; b = 33; c = +50;
Δ = b2-4ac
Δ = 332-4·2·50
Δ = 689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{689}}{2*2}=\frac{-33-\sqrt{689}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{689}}{2*2}=\frac{-33+\sqrt{689}}{4}
$