X+5/4x=27

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

X+5/4X=27

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


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}
$