1/8x+1/10x=1

Solution for 1/8x+1/10x=1 equation:

1/8x+1/10x=1

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


10x/80x^2+8x/80x^2-1=0

We multiply all the terms by the denominator


10x+8x-1*80x^2=0

We add all the numbers together, and all the variables

18x-1*80x^2=0

Wy multiply elements

-80x^2+18x=0

a = -80; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-80)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-80}=\frac{-36}{-160}
=9/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-80}=\frac{0}{-160}
=0
$