-6n^2-12(-11n+8)=-10(n-4)

Solution for -6n^2-12(-11n+8)=-10(n-4) equation:

-6n^2-12(-11n+8)=-10(n-4)

We move all terms to the left:

-6n^2-12(-11n+8)-(-10(n-4))=0

We multiply parentheses

-6n^2+132n-(-10(n-4))-96=0


We calculate terms in parentheses: -(-10(n-4)), so:

-10(n-4)

We multiply parentheses

-10n+40

Back to the equation:

-(-10n+40)


We get rid of parentheses

-6n^2+132n+10n-40-96=0

We add all the numbers together, and all the variables

-6n^2+142n-136=0

a = -6; b = 142; c = -136;
Δ = b2-4ac
Δ = 1422-4·(-6)·(-136)
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(142)-130}{2*-6}=\frac{-272}{-12}
=22+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(142)+130}{2*-6}=\frac{-12}{-12}
=1
$