2x-5=1/5x+7

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

2x-5=1/5x+7

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-35x-25x-1=0

We add all the numbers together, and all the variables

10x^2-60x-1=0

a = 10; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·10·(-1)
Δ = 3640
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:

$\sqrt{\Delta}=\sqrt{3640}=\sqrt{4*910}=\sqrt{4}*\sqrt{910}=2\sqrt{910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{910}}{2*10}=\frac{60-2\sqrt{910}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{910}}{2*10}=\frac{60+2\sqrt{910}}{20}
$