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2x+3/4x+1/4x+2-2=20-2
We move all terms to the left:
2x+3/4x+1/4x+2-2-(20-2)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
2x+3/4x+1/4x+2-2-18=0
We add all the numbers together, and all the variables
2x+3/4x+1/4x-18=0
We multiply all the terms by the denominator
2x*4x-18*4x+3+1=0
We add all the numbers together, and all the variables
2x*4x-18*4x+4=0
Wy multiply elements
8x^2-72x+4=0
a = 8; b = -72; c = +4;
Δ = b2-4ac
Δ = -722-4·8·4
Δ = 5056
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{79}}{2*8}=\frac{72-8\sqrt{79}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{79}}{2*8}=\frac{72+8\sqrt{79}}{16} $
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