10h+15/24h=40

Solution for 10h+15/24h=40 equation:

10h+15/24h=40

We move all terms to the left:

10h+15/24h-(40)=0


Domain of the equation: 24h!=0

h!=0/24

h!=0

h∈R


We multiply all the terms by the denominator


10h*24h-40*24h+15=0

Wy multiply elements

240h^2-960h+15=0

a = 240; b = -960; c = +15;
Δ = b2-4ac
Δ = -9602-4·240·15
Δ = 907200
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:

$\sqrt{\Delta}=\sqrt{907200}=\sqrt{129600*7}=\sqrt{129600}*\sqrt{7}=360\sqrt{7}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-360\sqrt{7}}{2*240}=\frac{960-360\sqrt{7}}{480}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+360\sqrt{7}}{2*240}=\frac{960+360\sqrt{7}}{480}
$