8(-3/2x+9)=-9(4/3x-8)

Solution for 8(-3/2x+9)=-9(4/3x-8) equation:

8(-3/2x+9)=-9(4/3x-8)

We move all terms to the left:

8(-3/2x+9)-(-9(4/3x-8))=0


Domain of the equation: 2x+9)!=0

x∈R



Domain of the equation: 3x-8))!=0

x∈R


We multiply parentheses

-24x-(-9(4/3x-8))+72=0

We multiply all the terms by the denominator


-24x*3x+72*3x-8))-(-9(4-8))=0

We add all the numbers together, and all the variables

-24x*3x+72*3x-8))-(-9(-4))=0

We add all the numbers together, and all the variables

-24x*3x+72*3x=0

Wy multiply elements

-72x^2+216x=0

a = -72; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·(-72)·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*-72}=\frac{-432}{-144}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*-72}=\frac{0}{-144}
=0
$