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3x-11/2x=3
We move all terms to the left:
3x-11/2x-(3)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
3x*2x-3*2x-11=0
Wy multiply elements
6x^2-6x-11=0
a = 6; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·6·(-11)
Δ = 300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10\sqrt{3}}{2*6}=\frac{6-10\sqrt{3}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10\sqrt{3}}{2*6}=\frac{6+10\sqrt{3}}{12} $
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