2x+4/3x=380

Solution for 2x+4/3x=380 equation:

2x+4/3x=380

We move all terms to the left:

2x+4/3x-(380)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-380*3x+4=0

Wy multiply elements

6x^2-1140x+4=0

a = 6; b = -1140; c = +4;
Δ = b2-4ac
Δ = -11402-4·6·4
Δ = 1299504
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:

$\sqrt{\Delta}=\sqrt{1299504}=\sqrt{16*81219}=\sqrt{16}*\sqrt{81219}=4\sqrt{81219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1140)-4\sqrt{81219}}{2*6}=\frac{1140-4\sqrt{81219}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1140)+4\sqrt{81219}}{2*6}=\frac{1140+4\sqrt{81219}}{12}
$