11/2(2h)+2h=15

Solution for 11/2(2h)+2h=15 equation:

11/2(2h)+2h=15

We move all terms to the left:

11/2(2h)+2h-(15)=0


Domain of the equation: 22h!=0

h!=0/22

h!=0

h∈R


We add all the numbers together, and all the variables

2h+11/22h-15=0

We multiply all the terms by the denominator


2h*22h-15*22h+11=0

Wy multiply elements

44h^2-330h+11=0

a = 44; b = -330; c = +11;
Δ = b2-4ac
Δ = -3302-4·44·11
Δ = 106964
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:

$\sqrt{\Delta}=\sqrt{106964}=\sqrt{484*221}=\sqrt{484}*\sqrt{221}=22\sqrt{221}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-22\sqrt{221}}{2*44}=\frac{330-22\sqrt{221}}{88}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+22\sqrt{221}}{2*44}=\frac{330+22\sqrt{221}}{88}
$