H(x)=2/3x+1

Solution for H(x)=2/3x+1 equation:

(H)=2/3H+1

We move all terms to the left:

(H)-(2/3H+1)=0


Domain of the equation: 3H+1)!=0

H∈R


We get rid of parentheses

H-2/3H-1=0

We multiply all the terms by the denominator


H*3H-1*3H-2=0

Wy multiply elements

3H^2-3H-2=0

a = 3; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·3·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{33}}{2*3}=\frac{3-\sqrt{33}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*3}=\frac{3+\sqrt{33}}{6}
$