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1/2x+5=2/5x-4
We move all terms to the left:
1/2x+5-(2/5x-4)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x-4)!=0We get rid of parentheses
x∈R
1/2x-2/5x+4+5=0
We calculate fractions
5x/10x^2+(-4x)/10x^2+4+5=0
We add all the numbers together, and all the variables
5x/10x^2+(-4x)/10x^2+9=0
We multiply all the terms by the denominator
5x+(-4x)+9*10x^2=0
Wy multiply elements
90x^2+5x+(-4x)=0
We get rid of parentheses
90x^2+5x-4x=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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