4n^2+3n=115

Solution for 4n^2+3n=115 equation:

4n^2+3n=115

We move all terms to the left:

4n^2+3n-(115)=0

a = 4; b = 3; c = -115;
Δ = b2-4ac
Δ = 32-4·4·(-115)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-43}{2*4}=\frac{-46}{8}
=-5+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+43}{2*4}=\frac{40}{8}
=5
$