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x+1/2x=3000
We move all terms to the left:
x+1/2x-(3000)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
x*2x-3000*2x+1=0
Wy multiply elements
2x^2-6000x+1=0
a = 2; b = -6000; c = +1;
Δ = b2-4ac
Δ = -60002-4·2·1
Δ = 35999992
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{35999992}=\sqrt{4*8999998}=\sqrt{4}*\sqrt{8999998}=2\sqrt{8999998}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6000)-2\sqrt{8999998}}{2*2}=\frac{6000-2\sqrt{8999998}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6000)+2\sqrt{8999998}}{2*2}=\frac{6000+2\sqrt{8999998}}{4} $
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