x^2=64/9-8x

Solution for x^2=64/9-8x equation:

x^2=64/9-8x

We move all terms to the left:

x^2-(64/9-8x)=0


Domain of the equation: 9-8x)!=0

We move all terms containing x to the left, all other terms to the right

-8x)!=-9

x!=-9/1

x!=-9

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2+8x-64/9=0

We multiply all the terms by the denominator


x^2*9+8x*9-64=0

Wy multiply elements

9x^2+72x-64=0

a = 9; b = 72; c = -64;
Δ = b2-4ac
Δ = 722-4·9·(-64)
Δ = 7488
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:

$\sqrt{\Delta}=\sqrt{7488}=\sqrt{576*13}=\sqrt{576}*\sqrt{13}=24\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{13}}{2*9}=\frac{-72-24\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{13}}{2*9}=\frac{-72+24\sqrt{13}}{18}
$