3x+1/2x=60

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Solution for 3x+1/2x=60 equation: 



3x+1/2x=60

We move all terms to the left:

3x+1/2x-(60)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We multiply all the terms by the denominator


3x*2x-60*2x+1=0

Wy multiply elements

6x^2-120x+1=0

a = 6; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·6·1
Δ = 14376
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:


$\sqrt{\Delta}=\sqrt{14376}=\sqrt{4*3594}=\sqrt{4}*\sqrt{3594}=2\sqrt{3594}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3594}}{2*6}=\frac{120-2\sqrt{3594}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3594}}{2*6}=\frac{120+2\sqrt{3594}}{12}
$

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