x/10x+9=2x-7

Solution for x/10x+9=2x-7 equation:

x/10x+9=2x-7

We move all terms to the left:

x/10x+9-(2x-7)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

x/10x-2x+7+9=0

We multiply all the terms by the denominator


x-2x*10x+7*10x+9*10x=0

Wy multiply elements

-20x^2+x+70x+90x=0

We add all the numbers together, and all the variables

-20x^2+161x=0

a = -20; b = 161; c = 0;
Δ = b2-4ac
Δ = 1612-4·(-20)·0
Δ = 25921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25921}=161$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(161)-161}{2*-20}=\frac{-322}{-40}
=8+1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(161)+161}{2*-20}=\frac{0}{-40}
=0
$