(2)(x-15)=(5/2x)(2)

Solution for (2)(x-15)=(5/2x)(2) equation:

(2)(x-15)=(5/2x)(2)

We move all terms to the left:

(2)(x-15)-((5/2x)(2))=0


Domain of the equation: 2x)2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(x-15)-((+5/2x)2)=0

We multiply parentheses

2x-((+5/2x)2)-30=0

We multiply all the terms by the denominator


2x*2x)2)-((-30*2x)2)+5=0

Wy multiply elements

4x^2-60x=0

a = 4; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·4·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*4}=\frac{120}{8}
=15
$