5/6h-7/12=-3/4h-13

Solution for 5/6h-7/12=-3/4h-13 equation:

5/6h-7/12=-3/4h-13

We move all terms to the left:

5/6h-7/12-(-3/4h-13)=0


Domain of the equation: 6h!=0

h!=0/6

h!=0

h∈R



Domain of the equation: 4h-13)!=0

h∈R


We get rid of parentheses

5/6h+3/4h+13-7/12=0

We calculate fractions


(-672h^2)/288h^2+240h/288h^2+216h/288h^2+13=0

We multiply all the terms by the denominator


(-672h^2)+240h+216h+13*288h^2=0

We add all the numbers together, and all the variables

(-672h^2)+456h+13*288h^2=0

Wy multiply elements

(-672h^2)+3744h^2+456h=0

We get rid of parentheses

-672h^2+3744h^2+456h=0

We add all the numbers together, and all the variables

3072h^2+456h=0

a = 3072; b = 456; c = 0;
Δ = b2-4ac
Δ = 4562-4·3072·0
Δ = 207936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{207936}=456$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(456)-456}{2*3072}=\frac{-912}{6144}
=-19/128
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(456)+456}{2*3072}=\frac{0}{6144}
=0
$