5n2-12n=14

Solution for 5n2-12n=14 equation:

5n^2-12n=14

We move all terms to the left:

5n^2-12n-(14)=0

a = 5; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·5·(-14)
Δ = 424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{106}}{2*5}=\frac{12-2\sqrt{106}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{106}}{2*5}=\frac{12+2\sqrt{106}}{10}
$