X(4x-1)=14

Solution for X(4x-1)=14 equation:

X(4X-1)=14

We move all terms to the left:

X(4X-1)-(14)=0

We multiply parentheses

4X^2-1X-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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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