3x-4/4x=66

Solution for 3x-4/4x=66 equation:

3x-4/4x=66

We move all terms to the left:

3x-4/4x-(66)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


3x*4x-66*4x-4=0

Wy multiply elements

12x^2-264x-4=0

a = 12; b = -264; c = -4;
Δ = b2-4ac
Δ = -2642-4·12·(-4)
Δ = 69888
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:

$\sqrt{\Delta}=\sqrt{69888}=\sqrt{256*273}=\sqrt{256}*\sqrt{273}=16\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-16\sqrt{273}}{2*12}=\frac{264-16\sqrt{273}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+16\sqrt{273}}{2*12}=\frac{264+16\sqrt{273}}{24}
$