(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+62n-152=0

a = 30; b = 62; c = -152;
Δ = b2-4ac
Δ = 622-4·30·(-152)
Δ = 22084
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:

$\sqrt{\Delta}=\sqrt{22084}=\sqrt{4*5521}=\sqrt{4}*\sqrt{5521}=2\sqrt{5521}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{5521}}{2*30}=\frac{-62-2\sqrt{5521}}{60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{5521}}{2*30}=\frac{-62+2\sqrt{5521}}{60}
$