7.5/h=35h

Solution for 7.5/h=35h equation:

7.5/h=35h

We move all terms to the left:

7.5/h-(35h)=0


Domain of the equation: h!=0

h∈R


We add all the numbers together, and all the variables

-35h+7.5/h=0

We multiply all the terms by the denominator


-35h*h+7.5=0

Wy multiply elements

-35h^2+7.5=0

a = -35; b = 0; c = +7.5;
Δ = b2-4ac
Δ = 02-4·(-35)·7.5
Δ = 1050
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:

$\sqrt{\Delta}=\sqrt{1050}=\sqrt{25*42}=\sqrt{25}*\sqrt{42}=5\sqrt{42}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{42}}{2*-35}=\frac{0-5\sqrt{42}}{-70}
=-\frac{5\sqrt{42}}{-70}
=-\frac{\sqrt{42}}{-14}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{42}}{2*-35}=\frac{0+5\sqrt{42}}{-70}
=\frac{5\sqrt{42}}{-70}
=\frac{\sqrt{42}}{-14}
$