75=1/35^2h

Solution for 75=1/35^2h equation:

75=1/35^2h

We move all terms to the left:

75-(1/35^2h)=0


Domain of the equation: 35^2h)!=0

h!=0/1

h!=0

h∈R


We get rid of parentheses

-1/35^2h+75=0

We multiply all the terms by the denominator


75*35^2h-1=0

Wy multiply elements

2625h^2-1=0

a = 2625; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2625·(-1)
Δ = 10500
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:

$\sqrt{\Delta}=\sqrt{10500}=\sqrt{100*105}=\sqrt{100}*\sqrt{105}=10\sqrt{105}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{105}}{2*2625}=\frac{0-10\sqrt{105}}{5250}
=-\frac{10\sqrt{105}}{5250}
=-\frac{\sqrt{105}}{525}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{105}}{2*2625}=\frac{0+10\sqrt{105}}{5250}
=\frac{10\sqrt{105}}{5250}
=\frac{\sqrt{105}}{525}
$