3/2x+5x=13

Solution for 3/2x+5x=13 equation:

3/2x+5x=13

We move all terms to the left:

3/2x+5x-(13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x+3/2x-13=0

We multiply all the terms by the denominator


5x*2x-13*2x+3=0

Wy multiply elements

10x^2-26x+3=0

a = 10; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·10·3
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{139}}{2*10}=\frac{26-2\sqrt{139}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{139}}{2*10}=\frac{26+2\sqrt{139}}{20}
$