3(3n2-43)=745

Solution for 3(3n2-43)=745 equation:

3(3n^2-43)=745

We move all terms to the left:

3(3n^2-43)-(745)=0

We multiply parentheses

9n^2-129-745=0

We add all the numbers together, and all the variables

9n^2-874=0

a = 9; b = 0; c = -874;
Δ = b2-4ac
Δ = 02-4·9·(-874)
Δ = 31464
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:

$\sqrt{\Delta}=\sqrt{31464}=\sqrt{36*874}=\sqrt{36}*\sqrt{874}=6\sqrt{874}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{874}}{2*9}=\frac{0-6\sqrt{874}}{18}
=-\frac{6\sqrt{874}}{18}
=-\frac{\sqrt{874}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{874}}{2*9}=\frac{0+6\sqrt{874}}{18}
=\frac{6\sqrt{874}}{18}
=\frac{\sqrt{874}}{3}
$