4u^2-u-14=0

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

4u^2-u-14=0

We add all the numbers together, and all the variables

4u^2-1u-14=0

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

$\sqrt{\Delta}=\sqrt{225}=15$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*4}=\frac{-14}{8}
=-1+3/4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*4}=\frac{16}{8}
=2
$