X+30=5/3x

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

X+30=5/3X

We move all terms to the left:

X+30-(5/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+5/3X)+30=0

We get rid of parentheses

X-5/3X+30=0

We multiply all the terms by the denominator


X*3X+30*3X-5=0

Wy multiply elements

3X^2+90X-5=0

a = 3; b = 90; c = -5;
Δ = b2-4ac
Δ = 902-4·3·(-5)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-4\sqrt{510}}{2*3}=\frac{-90-4\sqrt{510}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+4\sqrt{510}}{2*3}=\frac{-90+4\sqrt{510}}{6}
$