H(x)=-4+1/3x

Solution for H(x)=-4+1/3x equation:

(H)=-4+1/3H

We move all terms to the left:

(H)-(-4+1/3H)=0


Domain of the equation: 3H)!=0

H!=0/1

H!=0

H∈R


We add all the numbers together, and all the variables

H-(1/3H-4)=0

We get rid of parentheses

H-1/3H+4=0

We multiply all the terms by the denominator


H*3H+4*3H-1=0

Wy multiply elements

3H^2+12H-1=0

a = 3; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·3·(-1)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{39}}{2*3}=\frac{-12-2\sqrt{39}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{39}}{2*3}=\frac{-12+2\sqrt{39}}{6}
$