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

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

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

We move all terms to the left:

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


Domain of the equation: 6h!=0

h!=0/6

h!=0

h∈R



Domain of the equation: 4h)!=0

h!=0/1

h!=0

h∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-672h^2+456h=0

a = -672; b = 456; c = 0;
Δ = b2-4ac
Δ = 4562-4·(-672)·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*-672}=\frac{-912}{-1344}
=19/28
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(456)+456}{2*-672}=\frac{0}{-1344}
=0
$