21n^2-7=46n

Solution for 21n^2-7=46n equation:

21n^2-7=46n

We move all terms to the left:

21n^2-7-(46n)=0

a = 21; b = -46; c = -7;
Δ = b2-4ac
Δ = -462-4·21·(-7)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-52}{2*21}=\frac{-6}{42}
=-1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+52}{2*21}=\frac{98}{42}
=2+1/3
$