8-1/4(h)=12-1/2(h)

Solution for 8-1/4(h)=12-1/2(h) equation:

8-1/4(h)=12-1/2(h)

We move all terms to the left:

8-1/4(h)-(12-1/2(h))=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R



Domain of the equation: 2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

-1/4h-(-1/2h+12)+8=0

We get rid of parentheses

-1/4h+1/2h-12+8=0

We calculate fractions


(-2h)/8h^2+4h/8h^2-12+8=0

We add all the numbers together, and all the variables

(-2h)/8h^2+4h/8h^2-4=0

We multiply all the terms by the denominator


(-2h)+4h-4*8h^2=0

We add all the numbers together, and all the variables

4h+(-2h)-4*8h^2=0

Wy multiply elements

-32h^2+4h+(-2h)=0

We get rid of parentheses

-32h^2+4h-2h=0

We add all the numbers together, and all the variables

-32h^2+2h=0

a = -32; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-32)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-32}=\frac{-4}{-64}
=1/16
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-32}=\frac{0}{-64}
=0
$