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2x=1/2x+3
We move all terms to the left:
2x-(1/2x+3)=0
Domain of the equation: 2x+3)!=0We get rid of parentheses
x∈R
2x-1/2x-3=0
We multiply all the terms by the denominator
2x*2x-3*2x-1=0
Wy multiply elements
4x^2-6x-1=0
a = 4; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·4·(-1)
Δ = 52
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*4}=\frac{6-2\sqrt{13}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*4}=\frac{6+2\sqrt{13}}{8} $
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