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X+3/2X-1=5
We move all terms to the left:
X+3/2X-1-(5)=0
Domain of the equation: 2X!=0We add all the numbers together, and all the variables
X!=0/2
X!=0
X∈R
X+3/2X-6=0
We multiply all the terms by the denominator
X*2X-6*2X+3=0
Wy multiply elements
2X^2-12X+3=0
a = 2; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·2·3
Δ = 120
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*2}=\frac{12-2\sqrt{30}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*2}=\frac{12+2\sqrt{30}}{4} $
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