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2/3x+x+5x=180
We move all terms to the left:
2/3x+x+5x-(180)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
6x+2/3x-180=0
We multiply all the terms by the denominator
6x*3x-180*3x+2=0
Wy multiply elements
18x^2-540x+2=0
a = 18; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·18·2
Δ = 291456
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{291456}=\sqrt{576*506}=\sqrt{576}*\sqrt{506}=24\sqrt{506}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-24\sqrt{506}}{2*18}=\frac{540-24\sqrt{506}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+24\sqrt{506}}{2*18}=\frac{540+24\sqrt{506}}{36} $
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