3/5x-5=1/10x+7

Solution for 3/5x-5=1/10x+7 equation:

3/5x-5=1/10x+7

We move all terms to the left:

3/5x-5-(1/10x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+7)!=0

x∈R


We get rid of parentheses

3/5x-1/10x-7-5=0

We calculate fractions


30x/50x^2+(-5x)/50x^2-7-5=0

We add all the numbers together, and all the variables

30x/50x^2+(-5x)/50x^2-12=0

We multiply all the terms by the denominator


30x+(-5x)-12*50x^2=0

Wy multiply elements

-600x^2+30x+(-5x)=0

We get rid of parentheses

-600x^2+30x-5x=0

We add all the numbers together, and all the variables

-600x^2+25x=0

a = -600; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-600)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-600}=\frac{-50}{-1200}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-600}=\frac{0}{-1200}
=0
$