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1/2x+10=x-2
We move all terms to the left:
1/2x+10-(x-2)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-x+2+10=0
We multiply all the terms by the denominator
-x*2x+2*2x+10*2x+1=0
Wy multiply elements
-2x^2+4x+20x+1=0
We add all the numbers together, and all the variables
-2x^2+24x+1=0
a = -2; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-2)·1
Δ = 584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{146}}{2*-2}=\frac{-24-2\sqrt{146}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{146}}{2*-2}=\frac{-24+2\sqrt{146}}{-4} $
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