x-3=105/3x-3

Solution for x-3=105/3x-3 equation:

x-3=105/3x-3

We move all terms to the left:

x-3-(105/3x-3)=0


Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

x-105/3x+3-3=0

We multiply all the terms by the denominator


x*3x+3*3x-3*3x-105=0

Wy multiply elements

3x^2+9x-9x-105=0

We add all the numbers together, and all the variables

3x^2-105=0

a = 3; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·3·(-105)
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*3}=\frac{0-6\sqrt{35}}{6}
=-\frac{6\sqrt{35}}{6}
=-\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*3}=\frac{0+6\sqrt{35}}{6}
=\frac{6\sqrt{35}}{6}
=\sqrt{35}
$