5/4x+x=27

Solution for 5/4x+x=27 equation:

5/4x+x=27

We move all terms to the left:

5/4x+x-(27)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/4x-27=0

We multiply all the terms by the denominator


x*4x-27*4x+5=0

Wy multiply elements

4x^2-108x+5=0

a = 4; b = -108; c = +5;
Δ = b2-4ac
Δ = -1082-4·4·5
Δ = 11584
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:

$\sqrt{\Delta}=\sqrt{11584}=\sqrt{64*181}=\sqrt{64}*\sqrt{181}=8\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-8\sqrt{181}}{2*4}=\frac{108-8\sqrt{181}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+8\sqrt{181}}{2*4}=\frac{108+8\sqrt{181}}{8}
$