x-27/4x=23

Solution for x-27/4x=23 equation:

x-27/4x=23

We move all terms to the left:

x-27/4x-(23)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-23*4x-27=0

Wy multiply elements

4x^2-92x-27=0

a = 4; b = -92; c = -27;
Δ = b2-4ac
Δ = -922-4·4·(-27)
Δ = 8896
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:

$\sqrt{\Delta}=\sqrt{8896}=\sqrt{64*139}=\sqrt{64}*\sqrt{139}=8\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-8\sqrt{139}}{2*4}=\frac{92-8\sqrt{139}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+8\sqrt{139}}{2*4}=\frac{92+8\sqrt{139}}{8}
$