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135*1/2x=143-1/4x
We move all terms to the left:
135*1/2x-(143-1/4x)=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
135*1/2x-(-1/4x+143)=0
We get rid of parentheses
135*1/2x+1/4x-143=0
We calculate fractions
2160x/8x^2+2x/8x^2-143=0
We multiply all the terms by the denominator
2160x+2x-143*8x^2=0
We add all the numbers together, and all the variables
2162x-143*8x^2=0
Wy multiply elements
-1144x^2+2162x=0
a = -1144; b = 2162; c = 0;
Δ = b2-4ac
Δ = 21622-4·(-1144)·0
Δ = 4674244
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{4674244}=2162$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2162)-2162}{2*-1144}=\frac{-4324}{-2288} =1+509/572 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2162)+2162}{2*-1144}=\frac{0}{-2288} =0 $
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