9/5h-4=h

Solution for 9/5h-4=h equation:

9/5h-4=h

We move all terms to the left:

9/5h-4-(h)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R


We add all the numbers together, and all the variables

-1h+9/5h-4=0

We multiply all the terms by the denominator


-1h*5h-4*5h+9=0

Wy multiply elements

-5h^2-20h+9=0

a = -5; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·(-5)·9
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{145}}{2*-5}=\frac{20-2\sqrt{145}}{-10}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{145}}{2*-5}=\frac{20+2\sqrt{145}}{-10}
$