5/4x=2.5x+6

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

5/4x=2.5x+6

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

5/4x-2.5x-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 = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{46}}{2*-8}=\frac{24-4\sqrt{46}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{46}}{2*-8}=\frac{24+4\sqrt{46}}{-16}
$