5/2x+31x=38

Solution for 5/2x+31x=38 equation:

5/2x+31x=38

We move all terms to the left:

5/2x+31x-(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

31x+5/2x-38=0

We multiply all the terms by the denominator


31x*2x-38*2x+5=0

Wy multiply elements

62x^2-76x+5=0

a = 62; b = -76; c = +5;
Δ = b2-4ac
Δ = -762-4·62·5
Δ = 4536
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:

$\sqrt{\Delta}=\sqrt{4536}=\sqrt{324*14}=\sqrt{324}*\sqrt{14}=18\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-18\sqrt{14}}{2*62}=\frac{76-18\sqrt{14}}{124}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+18\sqrt{14}}{2*62}=\frac{76+18\sqrt{14}}{124}
$