3/10x-7=1/8x

Solution for 3/10x-7=1/8x equation:

3/10x-7=1/8x

We move all terms to the left:

3/10x-7-(1/8x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/10x-(+1/8x)-7=0

We get rid of parentheses

3/10x-1/8x-7=0

We calculate fractions


24x/80x^2+(-10x)/80x^2-7=0

We multiply all the terms by the denominator


24x+(-10x)-7*80x^2=0

Wy multiply elements

-560x^2+24x+(-10x)=0

We get rid of parentheses

-560x^2+24x-10x=0

We add all the numbers together, and all the variables

-560x^2+14x=0

a = -560; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-560)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-560}=\frac{-28}{-1120}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-560}=\frac{0}{-1120}
=0
$