(2n-3)(6n+7)=0

Solution for (2n-3)(6n+7)=0 equation:

(2n-3)(6n+7)=0

We multiply parentheses ..

(+12n^2+14n-18n-21)=0

We get rid of parentheses

12n^2+14n-18n-21=0

We add all the numbers together, and all the variables

12n^2-4n-21=0

a = 12; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·12·(-21)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*12}=\frac{-28}{24}
=-1+1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*12}=\frac{36}{24}
=1+1/2
$