x+30=5/3x+18

Solution for x+30=5/3x+18 equation:

x+30=5/3x+18

We move all terms to the left:

x+30-(5/3x+18)=0


Domain of the equation: 3x+18)!=0

x∈R


We get rid of parentheses

x-5/3x-18+30=0

We multiply all the terms by the denominator


x*3x-18*3x+30*3x-5=0

Wy multiply elements

3x^2-54x+90x-5=0

We add all the numbers together, and all the variables

3x^2+36x-5=0

a = 3; b = 36; c = -5;
Δ = b2-4ac
Δ = 362-4·3·(-5)
Δ = 1356
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:

$\sqrt{\Delta}=\sqrt{1356}=\sqrt{4*339}=\sqrt{4}*\sqrt{339}=2\sqrt{339}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{339}}{2*3}=\frac{-36-2\sqrt{339}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{339}}{2*3}=\frac{-36+2\sqrt{339}}{6}
$