30-5/3x=2+3x

Solution for 30-5/3x=2+3x equation:

30-5/3x=2+3x

We move all terms to the left:

30-5/3x-(2+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+2)+30=0

We get rid of parentheses

-5/3x-3x-2+30=0

We multiply all the terms by the denominator


-3x*3x-2*3x+30*3x-5=0

Wy multiply elements

-9x^2-6x+90x-5=0

We add all the numbers together, and all the variables

-9x^2+84x-5=0

a = -9; b = 84; c = -5;
Δ = b2-4ac
Δ = 842-4·(-9)·(-5)
Δ = 6876
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:

$\sqrt{\Delta}=\sqrt{6876}=\sqrt{36*191}=\sqrt{36}*\sqrt{191}=6\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-6\sqrt{191}}{2*-9}=\frac{-84-6\sqrt{191}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+6\sqrt{191}}{2*-9}=\frac{-84+6\sqrt{191}}{-18}
$