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1/2x+2=3x-6
We move all terms to the left:
1/2x+2-(3x-6)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-3x+6+2=0
We multiply all the terms by the denominator
-3x*2x+6*2x+2*2x+1=0
Wy multiply elements
-6x^2+12x+4x+1=0
We add all the numbers together, and all the variables
-6x^2+16x+1=0
a = -6; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-6)·1
Δ = 280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{70}}{2*-6}=\frac{-16-2\sqrt{70}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{70}}{2*-6}=\frac{-16+2\sqrt{70}}{-12} $
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