6n^2=-40-53n

Solution for 6n^2=-40-53n equation:

6n^2=-40-53n

We move all terms to the left:

6n^2-(-40-53n)=0

We add all the numbers together, and all the variables

6n^2-(-53n-40)=0

We get rid of parentheses

6n^2+53n+40=0

a = 6; b = 53; c = +40;
Δ = b2-4ac
Δ = 532-4·6·40
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-43}{2*6}=\frac{-96}{12}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+43}{2*6}=\frac{-10}{12}
=-5/6
$