5n^2+7n+6=12

Solution for 5n^2+7n+6=12 equation:

5n^2+7n+6=12

We move all terms to the left:

5n^2+7n+6-(12)=0

We add all the numbers together, and all the variables

5n^2+7n-6=0

a = 5; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·5·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*5}=\frac{6}{10}
=3/5
$