H(x)=4/x-3

Solution for H(x)=4/x-3 equation:

(H)=4/H-3

We move all terms to the left:

(H)-(4/H-3)=0


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

H∈R


We get rid of parentheses

H-4/H+3=0

We multiply all the terms by the denominator


H*H+3*H-4=0

We add all the numbers together, and all the variables

3H+H*H-4=0

Wy multiply elements

H^2+3H-4=0

a = 1; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*1}=\frac{-8}{2}
=-4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*1}=\frac{2}{2}
=1
$