0=3n2+4n-7

Solution for 0=3n2+4n-7 equation:

0=3n^2+4n-7

We move all terms to the left:

0-(3n^2+4n-7)=0

We add all the numbers together, and all the variables

-(3n^2+4n-7)=0

We get rid of parentheses

-3n^2-4n+7=0

a = -3; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-3)·7
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*-3}=\frac{-6}{-6}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*-3}=\frac{14}{-6}
=-2+1/3
$