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1/2x-2x=3-5x
We move all terms to the left:
1/2x-2x-(3-5x)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
1/2x-2x-(-5x+3)=0
We add all the numbers together, and all the variables
-2x+1/2x-(-5x+3)=0
We get rid of parentheses
-2x+1/2x+5x-3=0
We multiply all the terms by the denominator
-2x*2x+5x*2x-3*2x+1=0
Wy multiply elements
-4x^2+10x^2-6x+1=0
We add all the numbers together, and all the variables
6x^2-6x+1=0
a = 6; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·6·1
Δ = 12
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*6}=\frac{6-2\sqrt{3}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*6}=\frac{6+2\sqrt{3}}{12} $
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