4n^2+6n-58=12

Solution for 4n^2+6n-58=12 equation:

4n^2+6n-58=12

We move all terms to the left:

4n^2+6n-58-(12)=0

We add all the numbers together, and all the variables

4n^2+6n-70=0

a = 4; b = 6; c = -70;
Δ = b2-4ac
Δ = 62-4·4·(-70)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-34}{2*4}=\frac{-40}{8}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+34}{2*4}=\frac{28}{8}
=3+1/2
$