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1/8x+1/5x+1/8=57/40
We move all terms to the left:
1/8x+1/5x+1/8-(57/40)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
1/8x+1/5x+1/8-(+57/40)=0
We get rid of parentheses
1/8x+1/5x+1/8-57/40=0
We calculate fractions
(-91200x^2)/102400x^2+800x/102400x^2+20480x/102400x^2+800x/102400x^2=0
We multiply all the terms by the denominator
(-91200x^2)+800x+20480x+800x=0
We add all the numbers together, and all the variables
(-91200x^2)+22080x=0
We get rid of parentheses
-91200x^2+22080x=0
a = -91200; b = 22080; c = 0;
Δ = b2-4ac
Δ = 220802-4·(-91200)·0
Δ = 487526400
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{487526400}=22080$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22080)-22080}{2*-91200}=\frac{-44160}{-182400} =23/95 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22080)+22080}{2*-91200}=\frac{0}{-182400} =0 $
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