1/4x+5x=37

Solution for 1/4x+5x=37 equation:

1/4x+5x=37

We move all terms to the left:

1/4x+5x-(37)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/4x-37=0

We multiply all the terms by the denominator


5x*4x-37*4x+1=0

Wy multiply elements

20x^2-148x+1=0

a = 20; b = -148; c = +1;
Δ = b2-4ac
Δ = -1482-4·20·1
Δ = 21824
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:

$\sqrt{\Delta}=\sqrt{21824}=\sqrt{64*341}=\sqrt{64}*\sqrt{341}=8\sqrt{341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-8\sqrt{341}}{2*20}=\frac{148-8\sqrt{341}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+8\sqrt{341}}{2*20}=\frac{148+8\sqrt{341}}{40}
$