(32x^2-8)/(10-x)=0

Solution for (32x^2-8)/(10-x)=0 equation:

(32x^2-8)/(10-x)=0


Domain of the equation: (10-x)!=0

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

-x!=-10

x!=-10/-1

x!=+10

x∈R


We add all the numbers together, and all the variables

(32x^2-8)/(-1x+10)=0

We multiply all the terms by the denominator


(32x^2-8)=0

We get rid of parentheses

32x^2-8=0

a = 32; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·32·(-8)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*32}=\frac{-32}{64}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*32}=\frac{32}{64}
=1/2
$