5/7x+3=x-3

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

5/7x+3=x-3

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

5/7x-x+3+3=0

We multiply all the terms by the denominator


-x*7x+3*7x+3*7x+5=0

Wy multiply elements

-7x^2+21x+21x+5=0

We add all the numbers together, and all the variables

-7x^2+42x+5=0

a = -7; b = 42; c = +5;
Δ = b2-4ac
Δ = 422-4·(-7)·5
Δ = 1904
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:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{119}}{2*-7}=\frac{-42-4\sqrt{119}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{119}}{2*-7}=\frac{-42+4\sqrt{119}}{-14}
$