5/4x+x=117

Solution for 5/4x+x=117 equation:

5/4x+x=117

We move all terms to the left:

5/4x+x-(117)=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-117=0

We multiply all the terms by the denominator


x*4x-117*4x+5=0

Wy multiply elements

4x^2-468x+5=0

a = 4; b = -468; c = +5;
Δ = b2-4ac
Δ = -4682-4·4·5
Δ = 218944
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:

$\sqrt{\Delta}=\sqrt{218944}=\sqrt{64*3421}=\sqrt{64}*\sqrt{3421}=8\sqrt{3421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-8\sqrt{3421}}{2*4}=\frac{468-8\sqrt{3421}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+8\sqrt{3421}}{2*4}=\frac{468+8\sqrt{3421}}{8}
$