8(-1/2x+8)=-9(2/3x-6)

Solution for 8(-1/2x+8)=-9(2/3x-6) equation:

8(-1/2x+8)=-9(2/3x-6)

We move all terms to the left:

8(-1/2x+8)-(-9(2/3x-6))=0


Domain of the equation: 2x+8)!=0

x∈R



Domain of the equation: 3x-6))!=0

x∈R


We multiply parentheses

-8x-(-9(2/3x-6))+64=0

We multiply all the terms by the denominator


-8x*3x+64*3x-6))-(-9(2-6))=0

We add all the numbers together, and all the variables

-8x*3x+64*3x-6))-(-9(-4))=0

We add all the numbers together, and all the variables

-8x*3x+64*3x=0

Wy multiply elements

-24x^2+192x=0

a = -24; b = 192; c = 0;
Δ = b2-4ac
Δ = 1922-4·(-24)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-192}{2*-24}=\frac{-384}{-48}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+192}{2*-24}=\frac{0}{-48}
=0
$