(5/2)x=25/4

Solution for (5/2)x=25/4 equation:

(5/2)x=25/4

We move all terms to the left:

(5/2)x-(25/4)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/2)x-(+25/4)=0

We multiply parentheses

5x^2-(+25/4)=0

We get rid of parentheses

5x^2-25/4=0

We multiply all the terms by the denominator


5x^2*4-25=0

Wy multiply elements

20x^2-25=0

a = 20; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·20·(-25)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*20}=\frac{0-20\sqrt{5}}{40}
=-\frac{20\sqrt{5}}{40}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*20}=\frac{0+20\sqrt{5}}{40}
=\frac{20\sqrt{5}}{40}
=\frac{\sqrt{5}}{2}
$