H(x)=x/5x+3

Solution for H(x)=x/5x+3 equation:

(H)=H/5H+3

We move all terms to the left:

(H)-(H/5H+3)=0


Domain of the equation: 5H+3)!=0

H∈R


We get rid of parentheses

H-H/5H-3=0

We multiply all the terms by the denominator


H*5H-H-3*5H=0

We add all the numbers together, and all the variables

-1H+H*5H-3*5H=0

Wy multiply elements

5H^2-1H-15H=0

We add all the numbers together, and all the variables

5H^2-16H=0

a = 5; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·5·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*5}=\frac{0}{10}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*5}=\frac{32}{10}
=3+1/5
$