5/2x+24x=38

Solution for 5/2x+24x=38 equation:

5/2x+24x=38

We move all terms to the left:

5/2x+24x-(38)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

24x+5/2x-38=0

We multiply all the terms by the denominator


24x*2x-38*2x+5=0

Wy multiply elements

48x^2-76x+5=0

a = 48; b = -76; c = +5;
Δ = b2-4ac
Δ = -762-4·48·5
Δ = 4816
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:

$\sqrt{\Delta}=\sqrt{4816}=\sqrt{16*301}=\sqrt{16}*\sqrt{301}=4\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{301}}{2*48}=\frac{76-4\sqrt{301}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{301}}{2*48}=\frac{76+4\sqrt{301}}{96}
$