3n*n-7n+2=0

Solution for 3n*n-7n+2=0 equation:

3n*n-7n+2=0

We add all the numbers together, and all the variables

-7n+3n*n+2=0

Wy multiply elements

3n^2-7n+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*3}=\frac{2}{6}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$