X+5/4x=54

Solution for X+5/4x=54 equation:

X+5/4X=54

We move all terms to the left:

X+5/4X-(54)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-54*4X+5=0

Wy multiply elements

4X^2-216X+5=0

a = 4; b = -216; c = +5;
Δ = b2-4ac
Δ = -2162-4·4·5
Δ = 46576
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:

$\sqrt{\Delta}=\sqrt{46576}=\sqrt{16*2911}=\sqrt{16}*\sqrt{2911}=4\sqrt{2911}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-4\sqrt{2911}}{2*4}=\frac{216-4\sqrt{2911}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+4\sqrt{2911}}{2*4}=\frac{216+4\sqrt{2911}}{8}
$