20n2+7n=201

Solution for 20n2+7n=201 equation:

20n^2+7n=201

We move all terms to the left:

20n^2+7n-(201)=0

a = 20; b = 7; c = -201;
Δ = b2-4ac
Δ = 72-4·20·(-201)
Δ = 16129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16129}=127$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-127}{2*20}=\frac{-134}{40}
=-3+7/20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+127}{2*20}=\frac{120}{40}
=3
$