4x-34=34+4/3x

Solution for 4x-34=34+4/3x equation:

4x-34=34+4/3x

We move all terms to the left:

4x-34-(34+4/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(4/3x+34)-34=0

We get rid of parentheses

4x-4/3x-34-34=0

We multiply all the terms by the denominator


4x*3x-34*3x-34*3x-4=0

Wy multiply elements

12x^2-102x-102x-4=0

We add all the numbers together, and all the variables

12x^2-204x-4=0

a = 12; b = -204; c = -4;
Δ = b2-4ac
Δ = -2042-4·12·(-4)
Δ = 41808
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:

$\sqrt{\Delta}=\sqrt{41808}=\sqrt{16*2613}=\sqrt{16}*\sqrt{2613}=4\sqrt{2613}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-4\sqrt{2613}}{2*12}=\frac{204-4\sqrt{2613}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+4\sqrt{2613}}{2*12}=\frac{204+4\sqrt{2613}}{24}
$