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2/5x+2=2/3x-4
We move all terms to the left:
2/5x+2-(2/3x-4)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x-4)!=0We get rid of parentheses
x∈R
2/5x-2/3x+4+2=0
We calculate fractions
6x/15x^2+(-10x)/15x^2+4+2=0
We add all the numbers together, and all the variables
6x/15x^2+(-10x)/15x^2+6=0
We multiply all the terms by the denominator
6x+(-10x)+6*15x^2=0
Wy multiply elements
90x^2+6x+(-10x)=0
We get rid of parentheses
90x^2+6x-10x=0
We add all the numbers together, and all the variables
90x^2-4x=0
a = 90; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·90·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*90}=\frac{0}{180} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*90}=\frac{8}{180} =2/45 $
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