12n^2-34n+9=12

Solution for 12n^2-34n+9=12 equation:

12n^2-34n+9=12

We move all terms to the left:

12n^2-34n+9-(12)=0

We add all the numbers together, and all the variables

12n^2-34n-3=0

a = 12; b = -34; c = -3;
Δ = b2-4ac
Δ = -342-4·12·(-3)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-10\sqrt{13}}{2*12}=\frac{34-10\sqrt{13}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+10\sqrt{13}}{2*12}=\frac{34+10\sqrt{13}}{24}
$