7n^2=70+21n

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

7n^2=70+21n

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

7n^2-21n-70=0

a = 7; b = -21; c = -70;
Δ = b2-4ac
Δ = -212-4·7·(-70)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-49}{2*7}=\frac{-28}{14}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+49}{2*7}=\frac{70}{14}
=5
$