5n^2-12n=22

Solution for 5n^2-12n=22 equation:

5n^2-12n=22

We move all terms to the left:

5n^2-12n-(22)=0

a = 5; b = -12; c = -22;
Δ = b2-4ac
Δ = -122-4·5·(-22)
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{146}}{2*5}=\frac{12-2\sqrt{146}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{146}}{2*5}=\frac{12+2\sqrt{146}}{10}
$