5x+5=1/5x+29

Solution for 5x+5=1/5x+29 equation:

5x+5=1/5x+29

We move all terms to the left:

5x+5-(1/5x+29)=0


Domain of the equation: 5x+29)!=0

x∈R


We get rid of parentheses

5x-1/5x-29+5=0

We multiply all the terms by the denominator


5x*5x-29*5x+5*5x-1=0

Wy multiply elements

25x^2-145x+25x-1=0

We add all the numbers together, and all the variables

25x^2-120x-1=0

a = 25; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·25·(-1)
Δ = 14500
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:

$\sqrt{\Delta}=\sqrt{14500}=\sqrt{100*145}=\sqrt{100}*\sqrt{145}=10\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-10\sqrt{145}}{2*25}=\frac{120-10\sqrt{145}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+10\sqrt{145}}{2*25}=\frac{120+10\sqrt{145}}{50}
$