1/2h+14=3/4h-2

Solution for 1/2h+14=3/4h-2 equation:

1/2h+14=3/4h-2

We move all terms to the left:

1/2h+14-(3/4h-2)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 4h-2)!=0

h∈R


We get rid of parentheses

1/2h-3/4h+2+14=0

We calculate fractions


4h/8h^2+(-6h)/8h^2+2+14=0

We add all the numbers together, and all the variables

4h/8h^2+(-6h)/8h^2+16=0

We multiply all the terms by the denominator


4h+(-6h)+16*8h^2=0

Wy multiply elements

128h^2+4h+(-6h)=0

We get rid of parentheses

128h^2+4h-6h=0

We add all the numbers together, and all the variables

128h^2-2h=0

a = 128; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·128·0
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*128}=\frac{0}{256}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*128}=\frac{4}{256}
=1/64
$