x=3x-3/6x+5

Solution for x=3x-3/6x+5 equation:

x=3x-3/6x+5

We move all terms to the left:

x-(3x-3/6x+5)=0


Domain of the equation: 6x+5)!=0

x∈R


We get rid of parentheses

x-3x+3/6x-5=0

We multiply all the terms by the denominator


x*6x-3x*6x-5*6x+3=0

Wy multiply elements

6x^2-18x^2-30x+3=0

We add all the numbers together, and all the variables

-12x^2-30x+3=0

a = -12; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·(-12)·3
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{29}}{2*-12}=\frac{30-6\sqrt{29}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{29}}{2*-12}=\frac{30+6\sqrt{29}}{-24}
$