5x+5=2/10x+29

Solution for 5x+5=2/10x+29 equation:

5x+5=2/10x+29

We move all terms to the left:

5x+5-(2/10x+29)=0


Domain of the equation: 10x+29)!=0

x∈R


We get rid of parentheses

5x-2/10x-29+5=0

We multiply all the terms by the denominator


5x*10x-29*10x+5*10x-2=0

Wy multiply elements

50x^2-290x+50x-2=0

We add all the numbers together, and all the variables

50x^2-240x-2=0

a = 50; b = -240; c = -2;
Δ = b2-4ac
Δ = -2402-4·50·(-2)
Δ = 58000
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:

$\sqrt{\Delta}=\sqrt{58000}=\sqrt{400*145}=\sqrt{400}*\sqrt{145}=20\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-20\sqrt{145}}{2*50}=\frac{240-20\sqrt{145}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+20\sqrt{145}}{2*50}=\frac{240+20\sqrt{145}}{100}
$