x(^-0.5)=3x(^-2.5)

Solution for x(^-0.5)=3x(^-2.5) equation:

x(^-0.5)=3x(^-2.5)

We move all terms to the left:

x(^-0.5)-(3x(^-2.5))=0

We multiply parentheses

x^2-0.5x-(3x(^-2.5))=0


We calculate terms in parentheses: -(3x(^-2.5)), so:

3x(^-2.5)

We multiply parentheses

3x^2-7.5x

Back to the equation:

-(3x^2-7.5x)


We get rid of parentheses

x^2-3x^2-0.5x+7.5x=0

We add all the numbers together, and all the variables

-2x^2+7x=0

a = -2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-2)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-2}=\frac{0}{-4}
=0
$