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3/4x+129=x
We move all terms to the left:
3/4x+129-(x)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
-1x+3/4x+129=0
We multiply all the terms by the denominator
-1x*4x+129*4x+3=0
Wy multiply elements
-4x^2+516x+3=0
a = -4; b = 516; c = +3;
Δ = b2-4ac
Δ = 5162-4·(-4)·3
Δ = 266304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{266304}=\sqrt{64*4161}=\sqrt{64}*\sqrt{4161}=8\sqrt{4161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(516)-8\sqrt{4161}}{2*-4}=\frac{-516-8\sqrt{4161}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(516)+8\sqrt{4161}}{2*-4}=\frac{-516+8\sqrt{4161}}{-8} $
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