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1/4x-3=6x
We move all terms to the left:
1/4x-3-(6x)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
-6x+1/4x-3=0
We multiply all the terms by the denominator
-6x*4x-3*4x+1=0
Wy multiply elements
-24x^2-12x+1=0
a = -24; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-24)·1
Δ = 240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-24}=\frac{12-4\sqrt{15}}{-48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-24}=\frac{12+4\sqrt{15}}{-48} $
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