4n^2-18n=6

Solution for 4n^2-18n=6 equation:

4n^2-18n=6

We move all terms to the left:

4n^2-18n-(6)=0

a = 4; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·4·(-6)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*4}=\frac{18-2\sqrt{105}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*4}=\frac{18+2\sqrt{105}}{8}
$