12-1/2h=18+2h

Solution for 12-1/2h=18+2h equation:

12-1/2h=18+2h

We move all terms to the left:

12-1/2h-(18+2h)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


We add all the numbers together, and all the variables

-1/2h-(2h+18)+12=0

We get rid of parentheses

-1/2h-2h-18+12=0

We multiply all the terms by the denominator


-2h*2h-18*2h+12*2h-1=0

Wy multiply elements

-4h^2-36h+24h-1=0

We add all the numbers together, and all the variables

-4h^2-12h-1=0

a = -4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-4)·(-1)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*-4}=\frac{12-8\sqrt{2}}{-8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*-4}=\frac{12+8\sqrt{2}}{-8}
$