39n^2+36n-42=0

Solution for 39n^2+36n-42=0 equation:

39n^2+36n-42=0

a = 39; b = 36; c = -42;
Δ = b2-4ac
Δ = 362-4·39·(-42)
Δ = 7848
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:

$\sqrt{\Delta}=\sqrt{7848}=\sqrt{36*218}=\sqrt{36}*\sqrt{218}=6\sqrt{218}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{218}}{2*39}=\frac{-36-6\sqrt{218}}{78}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{218}}{2*39}=\frac{-36+6\sqrt{218}}{78}
$