4n^2-3n=85

Solution for 4n^2-3n=85 equation:

4n^2-3n=85

We move all terms to the left:

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

a = 4; b = -3; c = -85;
Δ = b2-4ac
Δ = -32-4·4·(-85)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-37}{2*4}=\frac{-34}{8}
=-4+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+37}{2*4}=\frac{40}{8}
=5
$