2x+2(2/3)x=38

Solution for 2x+2(2/3)x=38 equation:

2x+2(2/3)x=38

We move all terms to the left:

2x+2(2/3)x-(38)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2(+2/3)x-38=0

We multiply parentheses

4x^2+2x-38=0

a = 4; b = 2; c = -38;
Δ = b2-4ac
Δ = 22-4·4·(-38)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{17}}{2*4}=\frac{-2-6\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{17}}{2*4}=\frac{-2+6\sqrt{17}}{8}
$