6n^2=14-5n

Solution for 6n^2=14-5n equation:

6n^2=14-5n

We move all terms to the left:

6n^2-(14-5n)=0

We add all the numbers together, and all the variables

6n^2-(-5n+14)=0

We get rid of parentheses

6n^2+5n-14=0

a = 6; b = 5; c = -14;
Δ = b2-4ac
Δ = 52-4·6·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*6}=\frac{-24}{12}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*6}=\frac{14}{12}
=1+1/6
$