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x-1=1/2x+2
We move all terms to the left:
x-1-(1/2x+2)=0
Domain of the equation: 2x+2)!=0We get rid of parentheses
x∈R
x-1/2x-2-1=0
We multiply all the terms by the denominator
x*2x-2*2x-1*2x-1=0
Wy multiply elements
2x^2-4x-2x-1=0
We add all the numbers together, and all the variables
2x^2-6x-1=0
a = 2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·2·(-1)
Δ = 44
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*2}=\frac{6-2\sqrt{11}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*2}=\frac{6+2\sqrt{11}}{4} $
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