3x-1/4x=56

Solution for 3x-1/4x=56 equation:

3x-1/4x=56

We move all terms to the left:

3x-1/4x-(56)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


3x*4x-56*4x-1=0

Wy multiply elements

12x^2-224x-1=0

a = 12; b = -224; c = -1;
Δ = b2-4ac
Δ = -2242-4·12·(-1)
Δ = 50224
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:

$\sqrt{\Delta}=\sqrt{50224}=\sqrt{16*3139}=\sqrt{16}*\sqrt{3139}=4\sqrt{3139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-4\sqrt{3139}}{2*12}=\frac{224-4\sqrt{3139}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+4\sqrt{3139}}{2*12}=\frac{224+4\sqrt{3139}}{24}
$