x^2+(32/12)x-64=0

Solution for x^2+(32/12)x-64=0 equation:

x^2+(32/12)x-64=0


Domain of the equation: 12)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2+(+32/12)x-64=0

We multiply parentheses

x^2+32x^2-64=0

We add all the numbers together, and all the variables

33x^2-64=0

a = 33; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·33·(-64)
Δ = 8448
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:

$\sqrt{\Delta}=\sqrt{8448}=\sqrt{256*33}=\sqrt{256}*\sqrt{33}=16\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{33}}{2*33}=\frac{0-16\sqrt{33}}{66}
=-\frac{16\sqrt{33}}{66}
=-\frac{8\sqrt{33}}{33}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{33}}{2*33}=\frac{0+16\sqrt{33}}{66}
=\frac{16\sqrt{33}}{66}
=\frac{8\sqrt{33}}{33}
$