3x+5=20-(1/2x)

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Solution for 3x+5=20-(1/2x) equation:



3x+5=20-(1/2x)
We move all terms to the left:
3x+5-(20-(1/2x))=0
Domain of the equation: 2x))!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3x-(20-(+1/2x))+5=0
We multiply all the terms by the denominator
3x*2x))-(20-(+5*2x))+1=0
Wy multiply elements
6x^2+10x=0
a = 6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·6·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*6}=\frac{-20}{12} =-1+2/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*6}=\frac{0}{12} =0 $

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