6x+5=5/2x

Solution for 6x+5=5/2x equation:

6x+5=5/2x

We move all terms to the left:

6x+5-(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

6x-(+5/2x)+5=0

We get rid of parentheses

6x-5/2x+5=0

We multiply all the terms by the denominator


6x*2x+5*2x-5=0

Wy multiply elements

12x^2+10x-5=0

a = 12; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·12·(-5)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*12}=\frac{-10-2\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*12}=\frac{-10+2\sqrt{85}}{24}
$