H(x)=5x-7/9x+2

Solution for H(x)=5x-7/9x+2 equation:

(H)=5H-7/9H+2

We move all terms to the left:

(H)-(5H-7/9H+2)=0


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

H∈R


We get rid of parentheses

H-5H+7/9H-2=0

We multiply all the terms by the denominator


H*9H-5H*9H-2*9H+7=0

Wy multiply elements

9H^2-45H^2-18H+7=0

We add all the numbers together, and all the variables

-36H^2-18H+7=0

a = -36; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·(-36)·7
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{37}}{2*-36}=\frac{18-6\sqrt{37}}{-72}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{37}}{2*-36}=\frac{18+6\sqrt{37}}{-72}
$