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4x-23=1/2x-2
We move all terms to the left:
4x-23-(1/2x-2)=0
Domain of the equation: 2x-2)!=0We get rid of parentheses
x∈R
4x-1/2x+2-23=0
We multiply all the terms by the denominator
4x*2x+2*2x-23*2x-1=0
Wy multiply elements
8x^2+4x-46x-1=0
We add all the numbers together, and all the variables
8x^2-42x-1=0
a = 8; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·8·(-1)
Δ = 1796
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1796}=\sqrt{4*449}=\sqrt{4}*\sqrt{449}=2\sqrt{449}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{449}}{2*8}=\frac{42-2\sqrt{449}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{449}}{2*8}=\frac{42+2\sqrt{449}}{16} $
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