(2x+13)(7x+19)=0

Solution for (2x+13)(7x+19)=0 equation:

(2x+13)(7x+19)=0

We multiply parentheses ..

(+14x^2+38x+91x+247)=0

We get rid of parentheses

14x^2+38x+91x+247=0

We add all the numbers together, and all the variables

14x^2+129x+247=0

a = 14; b = 129; c = +247;
Δ = b2-4ac
Δ = 1292-4·14·247
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(129)-53}{2*14}=\frac{-182}{28}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(129)+53}{2*14}=\frac{-76}{28}
=-2+5/7
$