24-18x=20/16x

Solution for 24-18x=20/16x equation:

24-18x=20/16x

We move all terms to the left:

24-18x-(20/16x)=0


Domain of the equation: 16x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-18x-(+20/16x)+24=0

We get rid of parentheses

-18x-20/16x+24=0

We multiply all the terms by the denominator


-18x*16x+24*16x-20=0

Wy multiply elements

-288x^2+384x-20=0

a = -288; b = 384; c = -20;
Δ = b2-4ac
Δ = 3842-4·(-288)·(-20)
Δ = 124416
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:

$\sqrt{\Delta}=\sqrt{124416}=\sqrt{20736*6}=\sqrt{20736}*\sqrt{6}=144\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-144\sqrt{6}}{2*-288}=\frac{-384-144\sqrt{6}}{-576}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+144\sqrt{6}}{2*-288}=\frac{-384+144\sqrt{6}}{-576}
$