0.05x=1/4x-38

Solution for 0.05x=1/4x-38 equation:

0.05x=1/4x-38

We move all terms to the left:

0.05x-(1/4x-38)=0


Domain of the equation: 4x-38)!=0

x∈R


We get rid of parentheses

0.05x-1/4x+38=0

We multiply all the terms by the denominator


(0.05x)*4x+38*4x-1=0

We add all the numbers together, and all the variables

(+0.05x)*4x+38*4x-1=0

We multiply parentheses

0x^2+38*4x-1=0

Wy multiply elements

0x^2+152x-1=0

We add all the numbers together, and all the variables

x^2+152x-1=0

a = 1; b = 152; c = -1;
Δ = b2-4ac
Δ = 1522-4·1·(-1)
Δ = 23108
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:

$\sqrt{\Delta}=\sqrt{23108}=\sqrt{4*5777}=\sqrt{4}*\sqrt{5777}=2\sqrt{5777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(152)-2\sqrt{5777}}{2*1}=\frac{-152-2\sqrt{5777}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(152)+2\sqrt{5777}}{2*1}=\frac{-152+2\sqrt{5777}}{2}
$