2/4h-9(1/8h+2)=23

Solution for 2/4h-9(1/8h+2)=23 equation:

2/4h-9(1/8h+2)=23

We move all terms to the left:

2/4h-9(1/8h+2)-(23)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R



Domain of the equation: 8h+2)!=0

h∈R


We multiply parentheses

2/4h-9h-18-23=0

We multiply all the terms by the denominator


-9h*4h-18*4h-23*4h+2=0

Wy multiply elements

-36h^2-72h-92h+2=0

We add all the numbers together, and all the variables

-36h^2-164h+2=0

a = -36; b = -164; c = +2;
Δ = b2-4ac
Δ = -1642-4·(-36)·2
Δ = 27184
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:

$\sqrt{\Delta}=\sqrt{27184}=\sqrt{16*1699}=\sqrt{16}*\sqrt{1699}=4\sqrt{1699}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-164)-4\sqrt{1699}}{2*-36}=\frac{164-4\sqrt{1699}}{-72}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-164)+4\sqrt{1699}}{2*-36}=\frac{164+4\sqrt{1699}}{-72}
$