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3/2x+3=1x
We move all terms to the left:
3/2x+3-(1x)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-1x+3/2x+3=0
We multiply all the terms by the denominator
-1x*2x+3*2x+3=0
Wy multiply elements
-2x^2+6x+3=0
a = -2; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-2)·3
Δ = 60
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*-2}=\frac{-6-2\sqrt{15}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*-2}=\frac{-6+2\sqrt{15}}{-4} $
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