7n^2=70n+21n

Solution for 7n^2=70n+21n equation:

7n^2=70n+21n

We move all terms to the left:

7n^2-(70n+21n)=0

We add all the numbers together, and all the variables

7n^2-(+91n)=0

We get rid of parentheses

7n^2-91n=0

a = 7; b = -91; c = 0;
Δ = b2-4ac
Δ = -912-4·7·0
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-91}{2*7}=\frac{0}{14}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+91}{2*7}=\frac{182}{14}
=13
$