3/5x+1/8x=1

Solution for 3/5x+1/8x=1 equation:

3/5x+1/8x=1

We move all terms to the left:

3/5x+1/8x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


24x/40x^2+5x/40x^2-1=0

We multiply all the terms by the denominator


24x+5x-1*40x^2=0

We add all the numbers together, and all the variables

29x-1*40x^2=0

Wy multiply elements

-40x^2+29x=0

a = -40; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-40)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-40}=\frac{-58}{-80}
=29/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-40}=\frac{0}{-80}
=0
$