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

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

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

We multiply parentheses ..

(+49n^2-42n+35n-30)=0

We get rid of parentheses

49n^2-42n+35n-30=0

We add all the numbers together, and all the variables

49n^2-7n-30=0

a = 49; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·49·(-30)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-77}{2*49}=\frac{-70}{98}
=-5/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+77}{2*49}=\frac{84}{98}
=6/7
$