/5x-7=7x+4

Solution for /5x-7=7x+4 equation:

/5x-7=7x+4

We move all terms to the left:

/5x-7-(7x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

/5x-7x-4-7=0

We multiply all the terms by the denominator


-7x*5x-4*5x-7*5x+=0

We add all the numbers together, and all the variables

-7x*5x-4*5x-7*5x=0

Wy multiply elements

-35x^2-20x-35x=0

We add all the numbers together, and all the variables

-35x^2-55x=0

a = -35; b = -55; c = 0;
Δ = b2-4ac
Δ = -552-4·(-35)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-55}{2*-35}=\frac{0}{-70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+55}{2*-35}=\frac{110}{-70}
=-1+4/7
$