H(x)=4/5x

Solution for H(x)=4/5x equation:

(H)=4/5H

We move all terms to the left:

(H)-(4/5H)=0


Domain of the equation: 5H)!=0

H!=0/1

H!=0

H∈R


We add all the numbers together, and all the variables

H-(+4/5H)=0

We get rid of parentheses

H-4/5H=0

We multiply all the terms by the denominator


H*5H-4=0

Wy multiply elements

5H^2-4=0

a = 5; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·5·(-4)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*5}=\frac{0-4\sqrt{5}}{10}
=-\frac{4\sqrt{5}}{10}
=-\frac{2\sqrt{5}}{5}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*5}=\frac{0+4\sqrt{5}}{10}
=\frac{4\sqrt{5}}{10}
=\frac{2\sqrt{5}}{5}
$