6n^2=20-7n

Solution for 6n^2=20-7n equation:

6n^2=20-7n

We move all terms to the left:

6n^2-(20-7n)=0

We add all the numbers together, and all the variables

6n^2-(-7n+20)=0

We get rid of parentheses

6n^2+7n-20=0

a = 6; b = 7; c = -20;
Δ = b2-4ac
Δ = 72-4·6·(-20)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*6}=\frac{-30}{12}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*6}=\frac{16}{12}
=1+1/3
$