5^1/2x+2/3x=37

Solution for 5^1/2x+2/3x=37 equation:

5^1/2x+2/3x=37

We move all terms to the left:

5^1/2x+2/3x-(37)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x^2/6x^2+4x/6x^2-37=0

We multiply all the terms by the denominator


15x^2+4x-37*6x^2=0

Wy multiply elements

15x^2-222x^2+4x=0

We add all the numbers together, and all the variables

-207x^2+4x=0

a = -207; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-207)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-207}=\frac{-8}{-414}
=4/207
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-207}=\frac{0}{-414}
=0
$