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5/3x-1/3=13+42/18x
We move all terms to the left:
5/3x-1/3-(13+42/18x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 18x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/3x-(42/18x+13)-1/3=0
We get rid of parentheses
5/3x-42/18x-13-1/3=0
We calculate fractions
90x/486x^2+(-1134x)/486x^2+(-18x)/486x^2-13=0
We multiply all the terms by the denominator
90x+(-1134x)+(-18x)-13*486x^2=0
Wy multiply elements
-6318x^2+90x+(-1134x)+(-18x)=0
We get rid of parentheses
-6318x^2+90x-1134x-18x=0
We add all the numbers together, and all the variables
-6318x^2-1062x=0
a = -6318; b = -1062; c = 0;
Δ = b2-4ac
Δ = -10622-4·(-6318)·0
Δ = 1127844
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1127844}=1062$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1062)-1062}{2*-6318}=\frac{0}{-12636} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1062)+1062}{2*-6318}=\frac{2124}{-12636} =-59/351 $
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