3/7x-42=x/10x-9=9

Solution for 3/7x-42=x/10x-9=9 equation:

3/7x-42=x/10x-9=9

We move all terms to the left:

3/7x-42-(x/10x-9)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 10x-9)!=0

x∈R


We get rid of parentheses

3/7x-x/10x+9-42=0

We calculate fractions


(-7x^2)/70x^2+30x/70x^2+9-42=0

We add all the numbers together, and all the variables

(-7x^2)/70x^2+30x/70x^2-33=0

We multiply all the terms by the denominator


(-7x^2)+30x-33*70x^2=0

Wy multiply elements

(-7x^2)-2310x^2+30x=0

We get rid of parentheses

-7x^2-2310x^2+30x=0

We add all the numbers together, and all the variables

-2317x^2+30x=0

a = -2317; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-2317)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-2317}=\frac{-60}{-4634}
=30/2317
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-2317}=\frac{0}{-4634}
=0
$