7x+2=1/7x-5

Solution for 7x+2=1/7x-5 equation:

7x+2=1/7x-5

We move all terms to the left:

7x+2-(1/7x-5)=0


Domain of the equation: 7x-5)!=0

x∈R


We get rid of parentheses

7x-1/7x+5+2=0

We multiply all the terms by the denominator


7x*7x+5*7x+2*7x-1=0

Wy multiply elements

49x^2+35x+14x-1=0

We add all the numbers together, and all the variables

49x^2+49x-1=0

a = 49; b = 49; c = -1;
Δ = b2-4ac
Δ = 492-4·49·(-1)
Δ = 2597
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:

$\sqrt{\Delta}=\sqrt{2597}=\sqrt{49*53}=\sqrt{49}*\sqrt{53}=7\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-7\sqrt{53}}{2*49}=\frac{-49-7\sqrt{53}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+7\sqrt{53}}{2*49}=\frac{-49+7\sqrt{53}}{98}
$