4n^2-6n=3

Solution for 4n^2-6n=3 equation:

4n^2-6n=3

We move all terms to the left:

4n^2-6n-(3)=0

a = 4; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·4·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*4}=\frac{6-2\sqrt{21}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*4}=\frac{6+2\sqrt{21}}{8}
$