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3x+12=1/2x+2
We move all terms to the left:
3x+12-(1/2x+2)=0
Domain of the equation: 2x+2)!=0We get rid of parentheses
x∈R
3x-1/2x-2+12=0
We multiply all the terms by the denominator
3x*2x-2*2x+12*2x-1=0
Wy multiply elements
6x^2-4x+24x-1=0
We add all the numbers together, and all the variables
6x^2+20x-1=0
a = 6; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·6·(-1)
Δ = 424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{106}}{2*6}=\frac{-20-2\sqrt{106}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{106}}{2*6}=\frac{-20+2\sqrt{106}}{12} $
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