x-2/3x=34

Solution for x-2/3x=34 equation:

x-2/3x=34

We move all terms to the left:

x-2/3x-(34)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-34*3x-2=0

Wy multiply elements

3x^2-102x-2=0

a = 3; b = -102; c = -2;
Δ = b2-4ac
Δ = -1022-4·3·(-2)
Δ = 10428
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:

$\sqrt{\Delta}=\sqrt{10428}=\sqrt{4*2607}=\sqrt{4}*\sqrt{2607}=2\sqrt{2607}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{2607}}{2*3}=\frac{102-2\sqrt{2607}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{2607}}{2*3}=\frac{102+2\sqrt{2607}}{6}
$