5h-15/h=5

Solution for 5h-15/h=5 equation:

5h-15/h=5

We move all terms to the left:

5h-15/h-(5)=0


Domain of the equation: h!=0

h∈R


We multiply all the terms by the denominator


5h*h-5*h-15=0

We add all the numbers together, and all the variables

-5h+5h*h-15=0

Wy multiply elements

5h^2-5h-15=0

a = 5; b = -5; c = -15;
Δ = b2-4ac
Δ = -52-4·5·(-15)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{13}}{2*5}=\frac{5-5\sqrt{13}}{10}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{13}}{2*5}=\frac{5+5\sqrt{13}}{10}
$