5x=1/4x-38

Solution for 5x=1/4x-38 equation:

5x=1/4x-38

We move all terms to the left:

5x-(1/4x-38)=0


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

x∈R


We get rid of parentheses

5x-1/4x+38=0

We multiply all the terms by the denominator


5x*4x+38*4x-1=0

Wy multiply elements

20x^2+152x-1=0

a = 20; b = 152; c = -1;
Δ = b2-4ac
Δ = 1522-4·20·(-1)
Δ = 23184
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:

$\sqrt{\Delta}=\sqrt{23184}=\sqrt{144*161}=\sqrt{144}*\sqrt{161}=12\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(152)-12\sqrt{161}}{2*20}=\frac{-152-12\sqrt{161}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(152)+12\sqrt{161}}{2*20}=\frac{-152+12\sqrt{161}}{40}
$