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150-1/2x=120+1/4x
We move all terms to the left:
150-1/2x-(120+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
-1/2x-(1/4x+120)+150=0
We get rid of parentheses
-1/2x-1/4x-120+150=0
We calculate fractions
(-4x)/8x^2+(-2x)/8x^2-120+150=0
We add all the numbers together, and all the variables
(-4x)/8x^2+(-2x)/8x^2+30=0
We multiply all the terms by the denominator
(-4x)+(-2x)+30*8x^2=0
Wy multiply elements
240x^2+(-4x)+(-2x)=0
We get rid of parentheses
240x^2-4x-2x=0
We add all the numbers together, and all the variables
240x^2-6x=0
a = 240; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·240·0
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*240}=\frac{0}{480} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*240}=\frac{12}{480} =1/40 $
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