4n^2+3n=3

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

4n^2+3n=3

We move all terms to the left:

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

a = 4; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·4·(-3)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{57}}{2*4}=\frac{-3-\sqrt{57}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*4}=\frac{-3+\sqrt{57}}{8}
$