5/8x+2.5=3/8x+1.5+1.4x

Solution for 5/8x+2.5=3/8x+1.5+1.4x equation:

5/8x+2.5=3/8x+1.5+1.4x

We move all terms to the left:

5/8x+2.5-(3/8x+1.5+1.4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 8x+1.5+1.4x)!=0

We move all terms containing x to the left, all other terms to the right

8x+1.4x)!=-1.5

x∈R


We add all the numbers together, and all the variables

5/8x-(1.4x+3/8x+1.5)+2.5=0

We get rid of parentheses

5/8x-1.4x-3/8x-1.5+2.5=0

We multiply all the terms by the denominator


-(1.4x)*8x-(1.5)*8x+(2.5)*8x+5-3=0

We add all the numbers together, and all the variables

-(+1.4x)*8x-(1.5)*8x+(2.5)*8x+5-3=0

We add all the numbers together, and all the variables

-(+1.4x)*8x-(1.5)*8x+(2.5)*8x+2=0

We multiply parentheses

-8x^2-12x+20x+2=0

We add all the numbers together, and all the variables

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

a = -8; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-8)·2
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*-8}=\frac{-8-8\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*-8}=\frac{-8+8\sqrt{2}}{-16}
$