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1/4x-(-1/2x)=-6
We move all terms to the left:
1/4x-(-1/2x)-(-6)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/4x-(-1/2x)+6=0
We get rid of parentheses
1/4x+1/2x+6=0
We calculate fractions
2x/8x^2+4x/8x^2+6=0
We multiply all the terms by the denominator
2x+4x+6*8x^2=0
We add all the numbers together, and all the variables
6x+6*8x^2=0
Wy multiply elements
48x^2+6x=0
a = 48; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·48·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*48}=\frac{-12}{96} =-1/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*48}=\frac{0}{96} =0 $
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