6-2.5x=5/4x

Solution for 6-2.5x=5/4x equation:

6-2.5x=5/4x

We move all terms to the left:

6-2.5x-(5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2.5x-(+5/4x)+6=0

We get rid of parentheses

-2.5x-5/4x+6=0

We multiply all the terms by the denominator


-(2.5x)*4x+6*4x-5=0

We add all the numbers together, and all the variables

-(+2.5x)*4x+6*4x-5=0

We multiply parentheses

-8x^2+6*4x-5=0

Wy multiply elements

-8x^2+24x-5=0

a = -8; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·(-8)·(-5)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{26}}{2*-8}=\frac{-24-4\sqrt{26}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{26}}{2*-8}=\frac{-24+4\sqrt{26}}{-16}
$