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3/2x-5/8=1/4x
We move all terms to the left:
3/2x-5/8-(1/4x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/2x-(+1/4x)-5/8=0
We get rid of parentheses
3/2x-1/4x-5/8=0
We calculate fractions
(-160x^2)/512x^2+768x/512x^2+(-128x)/512x^2=0
We multiply all the terms by the denominator
(-160x^2)+768x+(-128x)=0
We get rid of parentheses
-160x^2+768x-128x=0
We add all the numbers together, and all the variables
-160x^2+640x=0
a = -160; b = 640; c = 0;
Δ = b2-4ac
Δ = 6402-4·(-160)·0
Δ = 409600
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{409600}=640$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-640}{2*-160}=\frac{-1280}{-320} =+4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+640}{2*-160}=\frac{0}{-320} =0 $
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