5-1.5x=5/8x+2

Solution for 5-1.5x=5/8x+2 equation:

5-1.5x=5/8x+2

We move all terms to the left:

5-1.5x-(5/8x+2)=0


Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

-1.5x-5/8x-2+5=0

We multiply all the terms by the denominator


-(1.5x)*8x-2*8x+5*8x-5=0

We add all the numbers together, and all the variables

-(+1.5x)*8x-2*8x+5*8x-5=0

We multiply parentheses

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

Wy multiply elements

-8x^2-16x+40x-5=0

We add all the numbers together, and all the variables

-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}
$