H(x)=2x-6/x+5

Solution for H(x)=2x-6/x+5 equation:

(H)=2H-6/H+5

We move all terms to the left:

(H)-(2H-6/H+5)=0


Domain of the equation: H+5)!=0

H∈R


We get rid of parentheses

H-2H+6/H-5=0

We multiply all the terms by the denominator


H*H-2H*H-5*H+6=0

We add all the numbers together, and all the variables

-5H+H*H-2H*H+6=0

Wy multiply elements

H^2-2H^2-5H+6=0

We add all the numbers together, and all the variables

-1H^2-5H+6=0

a = -1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-1)·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-1}=\frac{-2}{-2}
=1
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-1}=\frac{12}{-2}
=-6
$