(5n-4)(6n+7=0)

Solution for (5n-4)(6n+7=0) equation:

(5n-4)(6n+7=0)

We move all terms to the left:

(5n-4)(6n+7-(0))=0

We add all the numbers together, and all the variables

(5n-4)(6n+7)=0

We multiply parentheses ..

(+30n^2+35n-24n-28)=0

We get rid of parentheses

30n^2+35n-24n-28=0

We add all the numbers together, and all the variables

30n^2+11n-28=0

a = 30; b = 11; c = -28;
Δ = b2-4ac
Δ = 112-4·30·(-28)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-59}{2*30}=\frac{-70}{60}
=-1+1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+59}{2*30}=\frac{48}{60}
=4/5
$