-5/2x=-1/8x-5

Solution for -5/2x=-1/8x-5 equation:

-5/2x=-1/8x-5

We move all terms to the left:

-5/2x-(-1/8x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

-5/2x+1/8x+5=0

We calculate fractions


(-40x)/16x^2+2x/16x^2+5=0

We multiply all the terms by the denominator


(-40x)+2x+5*16x^2=0

We add all the numbers together, and all the variables

2x+(-40x)+5*16x^2=0

Wy multiply elements

80x^2+2x+(-40x)=0

We get rid of parentheses

80x^2+2x-40x=0

We add all the numbers together, and all the variables

80x^2-38x=0

a = 80; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·80·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*80}=\frac{76}{160}
=19/40
$