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3x+6=2x+8+1/2x
We move all terms to the left:
3x+6-(2x+8+1/2x)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3x-(2x+1/2x+8)+6=0
We get rid of parentheses
3x-2x-1/2x-8+6=0
We multiply all the terms by the denominator
3x*2x-2x*2x-8*2x+6*2x-1=0
Wy multiply elements
6x^2-4x^2-16x+12x-1=0
We add all the numbers together, and all the variables
2x^2-4x-1=0
a = 2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·2·(-1)
Δ = 24
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*2}=\frac{4-2\sqrt{6}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*2}=\frac{4+2\sqrt{6}}{4} $
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