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3x-1/2x=12
We move all terms to the left:
3x-1/2x-(12)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
3x*2x-12*2x-1=0
Wy multiply elements
6x^2-24x-1=0
a = 6; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·6·(-1)
Δ = 600
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{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*6}=\frac{24-10\sqrt{6}}{12}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*6}=\frac{24+10\sqrt{6}}{12}
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