h=60-1/2h

Solution for h=60-1/2h equation:

h=60-1/2h

We move all terms to the left:

h-(60-1/2h)=0


Domain of the equation: 2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

h-(-1/2h+60)=0

We get rid of parentheses

h+1/2h-60=0

We multiply all the terms by the denominator


h*2h-60*2h+1=0

Wy multiply elements

2h^2-120h+1=0

a = 2; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·2·1
Δ = 14392
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:

$\sqrt{\Delta}=\sqrt{14392}=\sqrt{4*3598}=\sqrt{4}*\sqrt{3598}=2\sqrt{3598}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3598}}{2*2}=\frac{120-2\sqrt{3598}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3598}}{2*2}=\frac{120+2\sqrt{3598}}{4}
$