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3/5x-3=1/2x+5

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Solution for 3/5x-3=1/2x+5 equation:



3/5x-3=1/2x+5
We move all terms to the left:
3/5x-3-(1/2x+5)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x+5)!=0
x∈R
We get rid of parentheses
3/5x-1/2x-5-3=0
We calculate fractions
6x/10x^2+(-5x)/10x^2-5-3=0
We add all the numbers together, and all the variables
6x/10x^2+(-5x)/10x^2-8=0
We multiply all the terms by the denominator
6x+(-5x)-8*10x^2=0
Wy multiply elements
-80x^2+6x+(-5x)=0
We get rid of parentheses
-80x^2+6x-5x=0
We add all the numbers together, and all the variables
-80x^2+x=0
a = -80; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-80)·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*-80}=\frac{-2}{-160} =1/80
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-80}=\frac{0}{-160} =0

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