376h+12/h=280+15/h

Solution for 376h+12/h=280+15/h equation:

376h+12/h=280+15/h

We move all terms to the left:

376h+12/h-(280+15/h)=0


Domain of the equation: h!=0

h∈R



Domain of the equation: h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

376h+12/h-(15/h+280)=0

We get rid of parentheses

376h+12/h-15/h-280=0

We multiply all the terms by the denominator


376h*h-280*h+12-15=0

We add all the numbers together, and all the variables

-280h+376h*h-3=0

Wy multiply elements

376h^2-280h-3=0

a = 376; b = -280; c = -3;
Δ = b2-4ac
Δ = -2802-4·376·(-3)
Δ = 82912
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:

$\sqrt{\Delta}=\sqrt{82912}=\sqrt{16*5182}=\sqrt{16}*\sqrt{5182}=4\sqrt{5182}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-4\sqrt{5182}}{2*376}=\frac{280-4\sqrt{5182}}{752}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+4\sqrt{5182}}{2*376}=\frac{280+4\sqrt{5182}}{752}
$