x-4=5/3x

Solution for x-4=5/3x equation:

x-4=5/3x

We move all terms to the left:

x-4-(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)-4=0

We get rid of parentheses

x-5/3x-4=0

We multiply all the terms by the denominator


x*3x-4*3x-5=0

Wy multiply elements

3x^2-12x-5=0

a = 3; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·3·(-5)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*3}=\frac{12-2\sqrt{51}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*3}=\frac{12+2\sqrt{51}}{6}
$