5x+2/3x=126

Solution for 5x+2/3x=126 equation:

5x+2/3x=126

We move all terms to the left:

5x+2/3x-(126)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-126*3x+2=0

Wy multiply elements

15x^2-378x+2=0

a = 15; b = -378; c = +2;
Δ = b2-4ac
Δ = -3782-4·15·2
Δ = 142764
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:

$\sqrt{\Delta}=\sqrt{142764}=\sqrt{4*35691}=\sqrt{4}*\sqrt{35691}=2\sqrt{35691}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-2\sqrt{35691}}{2*15}=\frac{378-2\sqrt{35691}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+2\sqrt{35691}}{2*15}=\frac{378+2\sqrt{35691}}{30}
$