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3x-5=1/2x+0
We move all terms to the left:
3x-5-(1/2x+0)=0
Domain of the equation: 2x+0)!=0We add all the numbers together, and all the variables
x∈R
3x-(+1/2x)-5=0
We get rid of parentheses
3x-1/2x-5=0
We multiply all the terms by the denominator
3x*2x-5*2x-1=0
Wy multiply elements
6x^2-10x-1=0
a = 6; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·6·(-1)
Δ = 124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{31}}{2*6}=\frac{10-2\sqrt{31}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{31}}{2*6}=\frac{10+2\sqrt{31}}{12} $
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