5n2+3n=4

Solution for 5n2+3n=4 equation:

5n^2+3n=4

We move all terms to the left:

5n^2+3n-(4)=0

a = 5; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·5·(-4)
Δ = 89
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{89}}{2*5}=\frac{-3-\sqrt{89}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*5}=\frac{-3+\sqrt{89}}{10}
$