15n^2-8n=12

Solution for 15n^2-8n=12 equation:

15n^2-8n=12

We move all terms to the left:

15n^2-8n-(12)=0

a = 15; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·15·(-12)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*15}=\frac{-20}{30}
=-2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*15}=\frac{36}{30}
=1+1/5
$