7n*9n+12=190

Solution for 7n*9n+12=190 equation:

7n*9n+12=190

We move all terms to the left:

7n*9n+12-(190)=0

We add all the numbers together, and all the variables

7n*9n-178=0

Wy multiply elements

63n^2-178=0

a = 63; b = 0; c = -178;
Δ = b2-4ac
Δ = 02-4·63·(-178)
Δ = 44856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44856}=\sqrt{36*1246}=\sqrt{36}*\sqrt{1246}=6\sqrt{1246}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1246}}{2*63}=\frac{0-6\sqrt{1246}}{126}
=-\frac{6\sqrt{1246}}{126}
=-\frac{\sqrt{1246}}{21}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1246}}{2*63}=\frac{0+6\sqrt{1246}}{126}
=\frac{6\sqrt{1246}}{126}
=\frac{\sqrt{1246}}{21}
$