3/7x+9=x-7

Solution for 3/7x+9=x-7 equation:

3/7x+9=x-7

We move all terms to the left:

3/7x+9-(x-7)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-x*7x+7*7x+9*7x+3=0

Wy multiply elements

-7x^2+49x+63x+3=0

We add all the numbers together, and all the variables

-7x^2+112x+3=0

a = -7; b = 112; c = +3;
Δ = b2-4ac
Δ = 1122-4·(-7)·3
Δ = 12628
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12628}=\sqrt{4*3157}=\sqrt{4}*\sqrt{3157}=2\sqrt{3157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-2\sqrt{3157}}{2*-7}=\frac{-112-2\sqrt{3157}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+2\sqrt{3157}}{2*-7}=\frac{-112+2\sqrt{3157}}{-14}
$