9/5x+5=x+8

Solution for 9/5x+5=x+8 equation:

9/5x+5=x+8

We move all terms to the left:

9/5x+5-(x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

9/5x-x-8+5=0

We multiply all the terms by the denominator


-x*5x-8*5x+5*5x+9=0

Wy multiply elements

-5x^2-40x+25x+9=0

We add all the numbers together, and all the variables

-5x^2-15x+9=0

a = -5; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·(-5)·9
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9\sqrt{5}}{2*-5}=\frac{15-9\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9\sqrt{5}}{2*-5}=\frac{15+9\sqrt{5}}{-10}
$