x/7x+20=x-10

Solution for x/7x+20=x-10 equation:

x/7x+20=x-10

We move all terms to the left:

x/7x+20-(x-10)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

x/7x-x+10+20=0

We multiply all the terms by the denominator


x-x*7x+10*7x+20*7x=0

Wy multiply elements

-7x^2+x+70x+140x=0

We add all the numbers together, and all the variables

-7x^2+211x=0

a = -7; b = 211; c = 0;
Δ = b2-4ac
Δ = 2112-4·(-7)·0
Δ = 44521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44521}=211$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(211)-211}{2*-7}=\frac{-422}{-14}
=30+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(211)+211}{2*-7}=\frac{0}{-14}
=0
$