x+4/3x+2/3x=180

Solution for x+4/3x+2/3x=180 equation:

x+4/3x+2/3x=180

We move all terms to the left:

x+4/3x+2/3x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-180*3x+4+2=0

We add all the numbers together, and all the variables

x*3x-180*3x+6=0

Wy multiply elements

3x^2-540x+6=0

a = 3; b = -540; c = +6;
Δ = b2-4ac
Δ = -5402-4·3·6
Δ = 291528
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:

$\sqrt{\Delta}=\sqrt{291528}=\sqrt{36*8098}=\sqrt{36}*\sqrt{8098}=6\sqrt{8098}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{8098}}{2*3}=\frac{540-6\sqrt{8098}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{8098}}{2*3}=\frac{540+6\sqrt{8098}}{6}
$