75x+10-0.5x=(1/8x+5)

Solution for 75x+10-0.5x=(1/8x+5) equation:

75x+10-0.5x=(1/8x+5)

We move all terms to the left:

75x+10-0.5x-((1/8x+5))=0


Domain of the equation: 8x+5))!=0

x∈R


We add all the numbers together, and all the variables

74.5x-((1/8x+5))+10=0

We multiply all the terms by the denominator


(74.5x)*8x+10*8x+5))-((1+5))=0

We add all the numbers together, and all the variables

(+74.5x)*8x+10*8x+5))-(6)=0

We add all the numbers together, and all the variables

(+74.5x)*8x+10*8x=0

We multiply parentheses

592x^2+10*8x=0

Wy multiply elements

592x^2+80x=0

a = 592; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·592·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*592}=\frac{-160}{1184}
=-5/37
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*592}=\frac{0}{1184}
=0
$