91/(2h-1)=h

Solution for 91/(2h-1)=h equation:

91/(2h-1)=h

We move all terms to the left:

91/(2h-1)-(h)=0


Domain of the equation: (2h-1)!=0

We move all terms containing h to the left, all other terms to the right

2h!=1

h!=1/2

h!=1/2

h∈R


We add all the numbers together, and all the variables

-1h+91/(2h-1)=0

We multiply all the terms by the denominator


-1h*(2h-1)+91=0

We multiply parentheses

-2h^2+1h+91=0

We add all the numbers together, and all the variables

-2h^2+h+91=0

a = -2; b = 1; c = +91;
Δ = b2-4ac
Δ = 12-4·(-2)·91
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-27}{2*-2}=\frac{-28}{-4}
=+7
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+27}{2*-2}=\frac{26}{-4}
=-6+1/2
$