(9/17)h=5/6

Solution for (9/17)h=5/6 equation:

(9/17)h=5/6

We move all terms to the left:

(9/17)h-(5/6)=0


Domain of the equation: 17)h!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

(+9/17)h-(+5/6)=0

We multiply parentheses

9h^2-(+5/6)=0

We get rid of parentheses

9h^2-5/6=0

We multiply all the terms by the denominator


9h^2*6-5=0

Wy multiply elements

54h^2-5=0

a = 54; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·54·(-5)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*54}=\frac{0-6\sqrt{30}}{108}
=-\frac{6\sqrt{30}}{108}
=-\frac{\sqrt{30}}{18}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*54}=\frac{0+6\sqrt{30}}{108}
=\frac{6\sqrt{30}}{108}
=\frac{\sqrt{30}}{18}
$