-7x-1=1/5x-73

Solution for -7x-1=1/5x-73 equation:

-7x-1=1/5x-73

We move all terms to the left:

-7x-1-(1/5x-73)=0


Domain of the equation: 5x-73)!=0

x∈R


We get rid of parentheses

-7x-1/5x+73-1=0

We multiply all the terms by the denominator


-7x*5x+73*5x-1*5x-1=0

Wy multiply elements

-35x^2+365x-5x-1=0

We add all the numbers together, and all the variables

-35x^2+360x-1=0

a = -35; b = 360; c = -1;
Δ = b2-4ac
Δ = 3602-4·(-35)·(-1)
Δ = 129460
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:

$\sqrt{\Delta}=\sqrt{129460}=\sqrt{4*32365}=\sqrt{4}*\sqrt{32365}=2\sqrt{32365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-2\sqrt{32365}}{2*-35}=\frac{-360-2\sqrt{32365}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+2\sqrt{32365}}{2*-35}=\frac{-360+2\sqrt{32365}}{-70}
$