2n^2=14-3n

Solution for 2n^2=14-3n equation:

2n^2=14-3n

We move all terms to the left:

2n^2-(14-3n)=0

We add all the numbers together, and all the variables

2n^2-(-3n+14)=0

We get rid of parentheses

2n^2+3n-14=0

a = 2; b = 3; c = -14;
Δ = b2-4ac
Δ = 32-4·2·(-14)
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{-(3)-11}{2*2}=\frac{-14}{4}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+11}{2*2}=\frac{8}{4}
=2
$