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3x+9=1/4x-4
We move all terms to the left:
3x+9-(1/4x-4)=0
Domain of the equation: 4x-4)!=0We get rid of parentheses
x∈R
3x-1/4x+4+9=0
We multiply all the terms by the denominator
3x*4x+4*4x+9*4x-1=0
Wy multiply elements
12x^2+16x+36x-1=0
We add all the numbers together, and all the variables
12x^2+52x-1=0
a = 12; b = 52; c = -1;
Δ = b2-4ac
Δ = 522-4·12·(-1)
Δ = 2752
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2752}=\sqrt{64*43}=\sqrt{64}*\sqrt{43}=8\sqrt{43}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-8\sqrt{43}}{2*12}=\frac{-52-8\sqrt{43}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+8\sqrt{43}}{2*12}=\frac{-52+8\sqrt{43}}{24} $
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