5n2-3n=26

Solution for 5n2-3n=26 equation:

5n^2-3n=26

We move all terms to the left:

5n^2-3n-(26)=0

a = 5; b = -3; c = -26;
Δ = b2-4ac
Δ = -32-4·5·(-26)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-23}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+23}{2*5}=\frac{26}{10}
=2+3/5
$