3n^2-14n=5

Solution for 3n^2-14n=5 equation:

3n^2-14n=5

We move all terms to the left:

3n^2-14n-(5)=0

a = 3; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·3·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*3}=\frac{-2}{6}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*3}=\frac{30}{6}
=5
$