6n(n+4)=5n-10

Solution for 6n(n+4)=5n-10 equation:

6n(n+4)=5n-10

We move all terms to the left:

6n(n+4)-(5n-10)=0

We multiply parentheses

6n^2+24n-(5n-10)=0

We get rid of parentheses

6n^2+24n-5n+10=0

We add all the numbers together, and all the variables

6n^2+19n+10=0

a = 6; b = 19; c = +10;
Δ = b2-4ac
Δ = 192-4·6·10
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*6}=\frac{-30}{12}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*6}=\frac{-8}{12}
=-2/3
$