1/2h-15=2h

Solution for 1/2h-15=2h equation:

1/2h-15=2h

We move all terms to the left:

1/2h-15-(2h)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


We add all the numbers together, and all the variables

-2h+1/2h-15=0

We multiply all the terms by the denominator


-2h*2h-15*2h+1=0

Wy multiply elements

-4h^2-30h+1=0

a = -4; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-4)·1
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*-4}=\frac{30-2\sqrt{229}}{-8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*-4}=\frac{30+2\sqrt{229}}{-8}
$