18/5x=1.6x+24

Solution for 18/5x=1.6x+24 equation:

18/5x=1.6x+24

We move all terms to the left:

18/5x-(1.6x+24)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

18/5x-1.6x-24=0

We multiply all the terms by the denominator


-(1.6x)*5x-24*5x+18=0

We add all the numbers together, and all the variables

-(+1.6x)*5x-24*5x+18=0

We multiply parentheses

-5x^2-24*5x+18=0

Wy multiply elements

-5x^2-120x+18=0

a = -5; b = -120; c = +18;
Δ = b2-4ac
Δ = -1202-4·(-5)·18
Δ = 14760
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:

$\sqrt{\Delta}=\sqrt{14760}=\sqrt{36*410}=\sqrt{36}*\sqrt{410}=6\sqrt{410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-6\sqrt{410}}{2*-5}=\frac{120-6\sqrt{410}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+6\sqrt{410}}{2*-5}=\frac{120+6\sqrt{410}}{-10}
$