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4/3x+2/3x+x=180
We move all terms to the left:
4/3x+2/3x+x-(180)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
x+4/3x+2/3x-180=0
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} $
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