5/9h=h+4

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

5/9h=h+4

We move all terms to the left:

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


Domain of the equation: 9h!=0

h!=0/9

h!=0

h∈R


We get rid of parentheses

5/9h-h-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9h^2-36h+5=0

a = -9; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·(-9)·5
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{41}}{2*-9}=\frac{36-6\sqrt{41}}{-18}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{41}}{2*-9}=\frac{36+6\sqrt{41}}{-18}
$