6n^2+19n-10=-3

Solution for 6n^2+19n-10=-3 equation:

6n^2+19n-10=-3

We move all terms to the left:

6n^2+19n-10-(-3)=0

We add all the numbers together, and all the variables

6n^2+19n-7=0

a = 6; b = 19; c = -7;
Δ = b2-4ac
Δ = 192-4·6·(-7)
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{-(19)-23}{2*6}=\frac{-42}{12}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*6}=\frac{4}{12}
=1/3
$