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5-3/5x=11-2/3x
We move all terms to the left:
5-3/5x-(11-2/3x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-3/5x-(-2/3x+11)+5=0
We get rid of parentheses
-3/5x+2/3x-11+5=0
We calculate fractions
(-9x)/15x^2+10x/15x^2-11+5=0
We add all the numbers together, and all the variables
(-9x)/15x^2+10x/15x^2-6=0
We multiply all the terms by the denominator
(-9x)+10x-6*15x^2=0
We add all the numbers together, and all the variables
10x+(-9x)-6*15x^2=0
Wy multiply elements
-90x^2+10x+(-9x)=0
We get rid of parentheses
-90x^2+10x-9x=0
We add all the numbers together, and all the variables
-90x^2+x=0
a = -90; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-90)·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-90}=\frac{-2}{-180} =1/90 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-90}=\frac{0}{-180} =0 $
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