33x-4=1/432x+56.

Solution for 33x-4=1/432x+56. equation:

33x-4=1/432x+56.

We move all terms to the left:

33x-4-(1/432x+56.)=0


Domain of the equation: 432x+56.)!=0

x∈R


We add all the numbers together, and all the variables

33x-(1/432x+56)-4=0

We get rid of parentheses

33x-1/432x-56-4=0

We multiply all the terms by the denominator


33x*432x-56*432x-4*432x-1=0

Wy multiply elements

14256x^2-24192x-1728x-1=0

We add all the numbers together, and all the variables

14256x^2-25920x-1=0

a = 14256; b = -25920; c = -1;
Δ = b2-4ac
Δ = -259202-4·14256·(-1)
Δ = 671903424
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:

$\sqrt{\Delta}=\sqrt{671903424}=\sqrt{5184*129611}=\sqrt{5184}*\sqrt{129611}=72\sqrt{129611}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25920)-72\sqrt{129611}}{2*14256}=\frac{25920-72\sqrt{129611}}{28512}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25920)+72\sqrt{129611}}{2*14256}=\frac{25920+72\sqrt{129611}}{28512}
$