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

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

(H)=3(-H/2)

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2H^2-1H=0

a = 2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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