(6n-4)(5n+7)=180

Solution for (6n-4)(5n+7)=180 equation:

(6n-4)(5n+7)=180

We move all terms to the left:

(6n-4)(5n+7)-(180)=0

We multiply parentheses ..

(+30n^2+42n-20n-28)-180=0

We get rid of parentheses

30n^2+42n-20n-28-180=0

We add all the numbers together, and all the variables

30n^2+22n-208=0

a = 30; b = 22; c = -208;
Δ = b2-4ac
Δ = 222-4·30·(-208)
Δ = 25444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{25444}=\sqrt{4*6361}=\sqrt{4}*\sqrt{6361}=2\sqrt{6361}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{6361}}{2*30}=\frac{-22-2\sqrt{6361}}{60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{6361}}{2*30}=\frac{-22+2\sqrt{6361}}{60}
$