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1/4x=12-x
We move all terms to the left:
1/4x-(12-x)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
1/4x-(-1x+12)=0
We get rid of parentheses
1/4x+1x-12=0
We multiply all the terms by the denominator
1x*4x-12*4x+1=0
Wy multiply elements
4x^2-48x+1=0
a = 4; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·4·1
Δ = 2288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{143}}{2*4}=\frac{48-4\sqrt{143}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{143}}{2*4}=\frac{48+4\sqrt{143}}{8} $
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