(20n^2+46n-84)=0

Solution for (20n^2+46n-84)=0 equation:

(20n^2+46n-84)=0

We get rid of parentheses

20n^2+46n-84=0

a = 20; b = 46; c = -84;
Δ = b2-4ac
Δ = 462-4·20·(-84)
Δ = 8836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8836}=94$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-94}{2*20}=\frac{-140}{40}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+94}{2*20}=\frac{48}{40}
=1+1/5
$