12n^2+8n=7

Solution for 12n^2+8n=7 equation:

12n^2+8n=7

We move all terms to the left:

12n^2+8n-(7)=0

a = 12; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·12·(-7)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-20}{2*12}=\frac{-28}{24}
=-1+1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+20}{2*12}=\frac{12}{24}
=1/2
$