7n^2-147=28n

Solution for 7n^2-147=28n equation:

7n^2-147=28n

We move all terms to the left:

7n^2-147-(28n)=0

a = 7; b = -28; c = -147;
Δ = b2-4ac
Δ = -282-4·7·(-147)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-70}{2*7}=\frac{-42}{14}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+70}{2*7}=\frac{98}{14}
=7
$