1/4x=3x-33

Solution for 1/4x=3x-33 equation:

1/4x=3x-33

We move all terms to the left:

1/4x-(3x-33)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-3x+33=0

We multiply all the terms by the denominator


-3x*4x+33*4x+1=0

Wy multiply elements

-12x^2+132x+1=0

a = -12; b = 132; c = +1;
Δ = b2-4ac
Δ = 1322-4·(-12)·1
Δ = 17472
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:

$\sqrt{\Delta}=\sqrt{17472}=\sqrt{64*273}=\sqrt{64}*\sqrt{273}=8\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-8\sqrt{273}}{2*-12}=\frac{-132-8\sqrt{273}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+8\sqrt{273}}{2*-12}=\frac{-132+8\sqrt{273}}{-24}
$