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3/4x+15/10=2/8x
We move all terms to the left:
3/4x+15/10-(2/8x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 8x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/4x-(+2/8x)+15/10=0
We get rid of parentheses
3/4x-2/8x+15/10=0
We calculate fractions
3840x^2/320x^2+240x/320x^2+(-80x)/320x^2=0
We multiply all the terms by the denominator
3840x^2+240x+(-80x)=0
We get rid of parentheses
3840x^2+240x-80x=0
We add all the numbers together, and all the variables
3840x^2+160x=0
a = 3840; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·3840·0
Δ = 25600
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{25600}=160$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*3840}=\frac{-320}{7680} =-1/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*3840}=\frac{0}{7680} =0 $
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