5/3x-10=1-3x

Solution for 5/3x-10=1-3x equation:

5/3x-10=1-3x

We move all terms to the left:

5/3x-10-(1-3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(-3x+1)-10=0

We get rid of parentheses

5/3x+3x-1-10=0

We multiply all the terms by the denominator


3x*3x-1*3x-10*3x+5=0

Wy multiply elements

9x^2-3x-30x+5=0

We add all the numbers together, and all the variables

9x^2-33x+5=0

a = 9; b = -33; c = +5;
Δ = b2-4ac
Δ = -332-4·9·5
Δ = 909
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:

$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{101}}{2*9}=\frac{33-3\sqrt{101}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{101}}{2*9}=\frac{33+3\sqrt{101}}{18}
$