H(x)=-1/2x+9

Solution for H(x)=-1/2x+9 equation:

(H)=-1/2H+9

We move all terms to the left:

(H)-(-1/2H+9)=0


Domain of the equation: 2H+9)!=0

H∈R


We get rid of parentheses

H+1/2H-9=0

We multiply all the terms by the denominator


H*2H-9*2H+1=0

Wy multiply elements

2H^2-18H+1=0

a = 2; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·2·1
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{79}}{2*2}=\frac{18-2\sqrt{79}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{79}}{2*2}=\frac{18+2\sqrt{79}}{4}
$