(X-5/2)8x=3x

Solution for (X-5/2)8x=3x equation:

(X-5/2)8X=3X

We move all terms to the left:

(X-5/2)8X-(3X)=0


Domain of the equation: 2)8X!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(+X-5/2)8X-3X=0

We add all the numbers together, and all the variables

-3X+(+X-5/2)8X=0

We multiply parentheses

8X^2-40X^2-3X=0

We add all the numbers together, and all the variables

-32X^2-3X=0

a = -32; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-32)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-32}=\frac{0}{-64}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-32}=\frac{6}{-64}
=-3/32
$