(2n+7)(7n-6)=0

Solution for (2n+7)(7n-6)=0 equation:

(2n+7)(7n-6)=0

We multiply parentheses ..

(+14n^2-12n+49n-42)=0

We get rid of parentheses

14n^2-12n+49n-42=0

We add all the numbers together, and all the variables

14n^2+37n-42=0

a = 14; b = 37; c = -42;
Δ = b2-4ac
Δ = 372-4·14·(-42)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-61}{2*14}=\frac{-98}{28}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+61}{2*14}=\frac{24}{28}
=6/7
$