H(x)=1/2x-14

Solution for H(x)=1/2x-14 equation:

(H)=1/2H-14

We move all terms to the left:

(H)-(1/2H-14)=0


Domain of the equation: 2H-14)!=0

H∈R


We get rid of parentheses

H-1/2H+14=0

We multiply all the terms by the denominator


H*2H+14*2H-1=0

Wy multiply elements

2H^2+28H-1=0

a = 2; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·2·(-1)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-6\sqrt{22}}{2*2}=\frac{-28-6\sqrt{22}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+6\sqrt{22}}{2*2}=\frac{-28+6\sqrt{22}}{4}
$