4n2-3=85

Solution for 4n2-3=85 equation:

4n^2-3=85

We move all terms to the left:

4n^2-3-(85)=0

We add all the numbers together, and all the variables

4n^2-88=0

a = 4; b = 0; c = -88;
Δ = b2-4ac
Δ = 02-4·4·(-88)
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{22}}{2*4}=\frac{0-8\sqrt{22}}{8}
=-\frac{8\sqrt{22}}{8}
=-\sqrt{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{22}}{2*4}=\frac{0+8\sqrt{22}}{8}
=\frac{8\sqrt{22}}{8}
=\sqrt{22}
$