5/8x-6.375x=1.5

Solution for 5/8x-6.375x=1.5 equation:

5/8x-6.375x=1.5

We move all terms to the left:

5/8x-6.375x-(1.5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-6.375x+5/8x-1.5=0

We multiply all the terms by the denominator


-(6.375x)*8x-(1.5)*8x+5=0

We add all the numbers together, and all the variables

-(+6.375x)*8x-(1.5)*8x+5=0

We multiply parentheses

-48x^2-12x+5=0

a = -48; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·(-48)·5
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{69}}{2*-48}=\frac{12-4\sqrt{69}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{69}}{2*-48}=\frac{12+4\sqrt{69}}{-96}
$