x(x+5)/4x+4=9/5

Solution for x(x+5)/4x+4=9/5 equation:

x(x+5)/4x+4=9/5

We move all terms to the left:

x(x+5)/4x+4-(9/5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x(x+5)/4x+4-(+9/5)=0

We get rid of parentheses

x(x+5)/4x+4-9/5=0

We calculate fractions


(5x^2+25x)/20x+(-36x)/20x+4=0

We multiply all the terms by the denominator


(5x^2+25x)+(-36x)+4*20x=0

Wy multiply elements

(5x^2+25x)+(-36x)+80x=0

We get rid of parentheses

5x^2+25x-36x+80x=0

We add all the numbers together, and all the variables

5x^2+69x=0

a = 5; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·5·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*5}=\frac{-138}{10}
=-13+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*5}=\frac{0}{10}
=0
$