H(x)=1/3x+11

Solution for H(x)=1/3x+11 equation:

(H)=1/3H+11

We move all terms to the left:

(H)-(1/3H+11)=0


Domain of the equation: 3H+11)!=0

H∈R


We get rid of parentheses

H-1/3H-11=0

We multiply all the terms by the denominator


H*3H-11*3H-1=0

Wy multiply elements

3H^2-33H-1=0

a = 3; b = -33; c = -1;
Δ = b2-4ac
Δ = -332-4·3·(-1)
Δ = 1101
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{-(-33)-\sqrt{1101}}{2*3}=\frac{33-\sqrt{1101}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1101}}{2*3}=\frac{33+\sqrt{1101}}{6}
$