x+5/4x=63

Solution for x+5/4x=63 equation:

x+5/4x=63

We move all terms to the left:

x+5/4x-(63)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-63*4x+5=0

Wy multiply elements

4x^2-252x+5=0

a = 4; b = -252; c = +5;
Δ = b2-4ac
Δ = -2522-4·4·5
Δ = 63424
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:

$\sqrt{\Delta}=\sqrt{63424}=\sqrt{64*991}=\sqrt{64}*\sqrt{991}=8\sqrt{991}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-8\sqrt{991}}{2*4}=\frac{252-8\sqrt{991}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+8\sqrt{991}}{2*4}=\frac{252+8\sqrt{991}}{8}
$