12+11/h=-18-4h

Solution for 12+11/h=-18-4h equation:

12+11/h=-18-4h

We move all terms to the left:

12+11/h-(-18-4h)=0


Domain of the equation: h!=0

h∈R


We add all the numbers together, and all the variables

11/h-(-4h-18)+12=0

We get rid of parentheses

11/h+4h+18+12=0

We multiply all the terms by the denominator


4h*h+18*h+12*h+11=0

We add all the numbers together, and all the variables

30h+4h*h+11=0

Wy multiply elements

4h^2+30h+11=0

a = 4; b = 30; c = +11;
Δ = b2-4ac
Δ = 302-4·4·11
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{181}}{2*4}=\frac{-30-2\sqrt{181}}{8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{181}}{2*4}=\frac{-30+2\sqrt{181}}{8}
$