2x+(2/3*2x)=290

Solution for 2x+(2/3*2x)=290 equation:

2x+(2/3*2x)=290

We move all terms to the left:

2x+(2/3*2x)-(290)=0


Domain of the equation: 3*2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+(+2/3*2x)-290=0

We get rid of parentheses

2x+2/3*2x-290=0

We multiply all the terms by the denominator


2x*3*2x-290*3*2x+2=0

Wy multiply elements

12x^2*2-1740x*2+2=0

Wy multiply elements

24x^2-3480x+2=0

a = 24; b = -3480; c = +2;
Δ = b2-4ac
Δ = -34802-4·24·2
Δ = 12110208
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:

$\sqrt{\Delta}=\sqrt{12110208}=\sqrt{64*189222}=\sqrt{64}*\sqrt{189222}=8\sqrt{189222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3480)-8\sqrt{189222}}{2*24}=\frac{3480-8\sqrt{189222}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3480)+8\sqrt{189222}}{2*24}=\frac{3480+8\sqrt{189222}}{48}
$