H(x)=-2/3(x)-3

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

(H)=-2/3(H)-3

We move all terms to the left:

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


Domain of the equation: 3H-3)!=0

H∈R


We get rid of parentheses

H+2/3H+3=0

We multiply all the terms by the denominator


H*3H+3*3H+2=0

Wy multiply elements

3H^2+9H+2=0

a = 3; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·3·2
Δ = 57
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{-(9)-\sqrt{57}}{2*3}=\frac{-9-\sqrt{57}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*3}=\frac{-9+\sqrt{57}}{6}
$