24+0.44x=19/1.69x

Solution for 24+0.44x=19/1.69x equation:

24+0.44x=19/1.69x

We move all terms to the left:

24+0.44x-(19/1.69x)=0


Domain of the equation: 1.69x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.44x-(+19/1.69x)+24=0

We get rid of parentheses

0.44x-19/1.69x+24=0

We multiply all the terms by the denominator


(0.44x)*1.69x+24*1.69x-19=0

We add all the numbers together, and all the variables

(+0.44x)*1.69x+24*1.69x-19=0

We multiply parentheses

0x^2+24*1.69x-19=0

Wy multiply elements

0x^2+24x-19=0

We add all the numbers together, and all the variables

x^2+24x-19=0

a = 1; b = 24; c = -19;
Δ = b2-4ac
Δ = 242-4·1·(-19)
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{163}}{2*1}=\frac{-24-2\sqrt{163}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{163}}{2*1}=\frac{-24+2\sqrt{163}}{2}
$