x/19.2x-15=7.5x+8.4

Solution for x/19.2x-15=7.5x+8.4 equation:

x/19.2x-15=7.5x+8.4

We move all terms to the left:

x/19.2x-15-(7.5x+8.4)=0


Domain of the equation: 19.2x!=0

x!=0/19.2

x!=0

x∈R


We get rid of parentheses

x/19.2x-7.5x-8.4-15=0

We multiply all the terms by the denominator


x-(7.5x)*19.2x-(8.4)*19.2x-15*19.2x=0

We add all the numbers together, and all the variables

x-(+7.5x)*19.2x-(8.4)*19.2x-15*19.2x=0

We multiply parentheses

-133x^2+x-159.6x-15*19.2x=0

Wy multiply elements

-133x^2+x-159.6x-285x=0

We add all the numbers together, and all the variables

-133x^2-443.6x=0

a = -133; b = -443.6; c = 0;
Δ = b2-4ac
Δ = -443.62-4·(-133)·0
Δ = 196780.96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-443.6)-\sqrt{196780.96}}{2*-133}=\frac{443.6-\sqrt{196780.96}}{-266}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-443.6)+\sqrt{196780.96}}{2*-133}=\frac{443.6+\sqrt{196780.96}}{-266}
$