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1/2x=20+x
We move all terms to the left:
1/2x-(20+x)=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-(x+20)=0
We get rid of parentheses
1/2x-x-20=0
We multiply all the terms by the denominator
-x*2x-20*2x+1=0
Wy multiply elements
-2x^2-40x+1=0
a = -2; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·(-2)·1
Δ = 1608
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1608}=\sqrt{4*402}=\sqrt{4}*\sqrt{402}=2\sqrt{402}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{402}}{2*-2}=\frac{40-2\sqrt{402}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{402}}{2*-2}=\frac{40+2\sqrt{402}}{-4} $
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