8/3x+5x=46

Solution for 8/3x+5x=46 equation:

8/3x+5x=46

We move all terms to the left:

8/3x+5x-(46)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x+8/3x-46=0

We multiply all the terms by the denominator


5x*3x-46*3x+8=0

Wy multiply elements

15x^2-138x+8=0

a = 15; b = -138; c = +8;
Δ = b2-4ac
Δ = -1382-4·15·8
Δ = 18564
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:

$\sqrt{\Delta}=\sqrt{18564}=\sqrt{4*4641}=\sqrt{4}*\sqrt{4641}=2\sqrt{4641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{4641}}{2*15}=\frac{138-2\sqrt{4641}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{4641}}{2*15}=\frac{138+2\sqrt{4641}}{30}
$