(7n-6)(6n+5)=0

Solution for (7n-6)(6n+5)=0 equation:

(7n-6)(6n+5)=0

We multiply parentheses ..

(+42n^2+35n-36n-30)=0

We get rid of parentheses

42n^2+35n-36n-30=0

We add all the numbers together, and all the variables

42n^2-1n-30=0

a = 42; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·42·(-30)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-71}{2*42}=\frac{-70}{84}
=-5/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+71}{2*42}=\frac{72}{84}
=6/7
$