4x=12/5x=

Solution for 4x=12/5x= equation:

4x=12/5x=

We move all terms to the left:

4x-(12/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+12/5x)=0

We get rid of parentheses

4x-12/5x=0

We multiply all the terms by the denominator


4x*5x-12=0

Wy multiply elements

20x^2-12=0

a = 20; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·20·(-12)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*20}=\frac{0-8\sqrt{15}}{40}
=-\frac{8\sqrt{15}}{40}
=-\frac{\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*20}=\frac{0+8\sqrt{15}}{40}
=\frac{8\sqrt{15}}{40}
=\frac{\sqrt{15}}{5}
$