x+2/3x=1880

Solution for x+2/3x=1880 equation:

x+2/3x=1880

We move all terms to the left:

x+2/3x-(1880)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-1880*3x+2=0

Wy multiply elements

3x^2-5640x+2=0

a = 3; b = -5640; c = +2;
Δ = b2-4ac
Δ = -56402-4·3·2
Δ = 31809576
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:

$\sqrt{\Delta}=\sqrt{31809576}=\sqrt{4*7952394}=\sqrt{4}*\sqrt{7952394}=2\sqrt{7952394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5640)-2\sqrt{7952394}}{2*3}=\frac{5640-2\sqrt{7952394}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5640)+2\sqrt{7952394}}{2*3}=\frac{5640+2\sqrt{7952394}}{6}
$