x-5/4x=14

Solution for x-5/4x=14 equation:

x-5/4x=14

We move all terms to the left:

x-5/4x-(14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-14*4x-5=0

Wy multiply elements

4x^2-56x-5=0

a = 4; b = -56; c = -5;
Δ = b2-4ac
Δ = -562-4·4·(-5)
Δ = 3216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3216}=\sqrt{16*201}=\sqrt{16}*\sqrt{201}=4\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{201}}{2*4}=\frac{56-4\sqrt{201}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{201}}{2*4}=\frac{56+4\sqrt{201}}{8}
$