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