5n2-3n=34

Solution for 5n2-3n=34 equation:

5n^2-3n=34

We move all terms to the left:

5n^2-3n-(34)=0

a = 5; b = -3; c = -34;
Δ = b2-4ac
Δ = -32-4·5·(-34)
Δ = 689
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{689}}{2*5}=\frac{3-\sqrt{689}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{689}}{2*5}=\frac{3+\sqrt{689}}{10}
$