4n^2-12n-7=0

Solution for 4n^2-12n-7=0 equation:

4n^2-12n-7=0

a = 4; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·4·(-7)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*4}=\frac{-4}{8}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*4}=\frac{28}{8}
=3+1/2
$