14z^2-z-4=0

Solution for 14z^2-z-4=0 equation:

14z^2-z-4=0

We add all the numbers together, and all the variables

14z^2-1z-4=0

a = 14; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·14·(-4)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*14}=\frac{-14}{28}
=-1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*14}=\frac{16}{28}
=4/7
$