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1/2x+3=4x+4
We move all terms to the left:
1/2x+3-(4x+4)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-4x-4+3=0
We multiply all the terms by the denominator
-4x*2x-4*2x+3*2x+1=0
Wy multiply elements
-8x^2-8x+6x+1=0
We add all the numbers together, and all the variables
-8x^2-2x+1=0
a = -8; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-8)·1
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-8}=\frac{-4}{-16} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-8}=\frac{8}{-16} =-1/2 $
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