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3/4x+x=12-1/4x
We move all terms to the left:
3/4x+x-(12-1/4x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/4x+x-(-1/4x+12)=0
We add all the numbers together, and all the variables
x+3/4x-(-1/4x+12)=0
We get rid of parentheses
x+3/4x+1/4x-12=0
We multiply all the terms by the denominator
x*4x-12*4x+3+1=0
We add all the numbers together, and all the variables
x*4x-12*4x+4=0
Wy multiply elements
4x^2-48x+4=0
a = 4; b = -48; c = +4;
Δ = b2-4ac
Δ = -482-4·4·4
Δ = 2240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{35}}{2*4}=\frac{48-8\sqrt{35}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{35}}{2*4}=\frac{48+8\sqrt{35}}{8} $
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