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2x-6=3/2x+1
We move all terms to the left:
2x-6-(3/2x+1)=0
Domain of the equation: 2x+1)!=0We get rid of parentheses
x∈R
2x-3/2x-1-6=0
We multiply all the terms by the denominator
2x*2x-1*2x-6*2x-3=0
Wy multiply elements
4x^2-2x-12x-3=0
We add all the numbers together, and all the variables
4x^2-14x-3=0
a = 4; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·4·(-3)
Δ = 244
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{61}}{2*4}=\frac{14-2\sqrt{61}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{61}}{2*4}=\frac{14+2\sqrt{61}}{8} $
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