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2/5x+10=3/2x+5
We move all terms to the left:
2/5x+10-(3/2x+5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x+5)!=0We get rid of parentheses
x∈R
2/5x-3/2x-5+10=0
We calculate fractions
4x/10x^2+(-15x)/10x^2-5+10=0
We add all the numbers together, and all the variables
4x/10x^2+(-15x)/10x^2+5=0
We multiply all the terms by the denominator
4x+(-15x)+5*10x^2=0
Wy multiply elements
50x^2+4x+(-15x)=0
We get rid of parentheses
50x^2+4x-15x=0
We add all the numbers together, and all the variables
50x^2-11x=0
a = 50; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·50·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*50}=\frac{0}{100} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*50}=\frac{22}{100} =11/50 $
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