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3x+1/2x+3=18
We move all terms to the left:
3x+1/2x+3-(18)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3x+1/2x-15=0
We multiply all the terms by the denominator
3x*2x-15*2x+1=0
Wy multiply elements
6x^2-30x+1=0
a = 6; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·6·1
Δ = 876
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*6}=\frac{30-2\sqrt{219}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*6}=\frac{30+2\sqrt{219}}{12} $
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