2.6(2x+3)=5/2x

Solution for 2.6(2x+3)=5/2x equation:

2.6(2x+3)=5/2x

We move all terms to the left:

2.6(2x+3)-(5/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2.6(2x+3)-(+5/2x)=0

We multiply parentheses

5.2x-(+5/2x)+7.8=0

We get rid of parentheses

5.2x-5/2x+7.8=0

We multiply all the terms by the denominator


(5.2x)*2x+(7.8)*2x-5=0

We add all the numbers together, and all the variables

(+5.2x)*2x+(7.8)*2x-5=0

We multiply parentheses

10x^2+15.6x-5=0

a = 10; b = 15.6; c = -5;
Δ = b2-4ac
Δ = 15.62-4·10·(-5)
Δ = 443.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15.6)-\sqrt{443.36}}{2*10}=\frac{-15.6-\sqrt{443.36}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15.6)+\sqrt{443.36}}{2*10}=\frac{-15.6+\sqrt{443.36}}{20}
$