5x+2/3x=10

Solution for 5x+2/3x=10 equation:

5x+2/3x=10

We move all terms to the left:

5x+2/3x-(10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-10*3x+2=0

Wy multiply elements

15x^2-30x+2=0

a = 15; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·15·2
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{195}}{2*15}=\frac{30-2\sqrt{195}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{195}}{2*15}=\frac{30+2\sqrt{195}}{30}
$