(8/9x)-(1/2)=-2/3x+16

Solution for (8/9x)-(1/2)=-2/3x+16 equation:

(8/9x)-(1/2)=-2/3x+16

We move all terms to the left:

(8/9x)-(1/2)-(-2/3x+16)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x+16)!=0

x∈R


We add all the numbers together, and all the variables

(+8/9x)-(-2/3x+16)-(+1/2)=0

We get rid of parentheses

8/9x+2/3x-16-1/2=0

We calculate fractions


(-81x^2)/108x^2+96x/108x^2+72x/108x^2-16=0

We multiply all the terms by the denominator


(-81x^2)+96x+72x-16*108x^2=0

We add all the numbers together, and all the variables

(-81x^2)+168x-16*108x^2=0

Wy multiply elements

(-81x^2)-1728x^2+168x=0

We get rid of parentheses

-81x^2-1728x^2+168x=0

We add all the numbers together, and all the variables

-1809x^2+168x=0

a = -1809; b = 168; c = 0;
Δ = b2-4ac
Δ = 1682-4·(-1809)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-168}{2*-1809}=\frac{-336}{-3618}
=56/603
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+168}{2*-1809}=\frac{0}{-3618}
=0
$