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14+2x=3/2x+12
We move all terms to the left:
14+2x-(3/2x+12)=0
Domain of the equation: 2x+12)!=0We get rid of parentheses
x∈R
2x-3/2x-12+14=0
We multiply all the terms by the denominator
2x*2x-12*2x+14*2x-3=0
Wy multiply elements
4x^2-24x+28x-3=0
We add all the numbers together, and all the variables
4x^2+4x-3=0
a = 4; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·4·(-3)
Δ = 64
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*4}=\frac{-12}{8} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*4}=\frac{4}{8} =1/2 $
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