1/2h+6(h-9)=63

Solution for 1/2h+6(h-9)=63 equation:

1/2h+6(h-9)=63

We move all terms to the left:

1/2h+6(h-9)-(63)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


We multiply parentheses

1/2h+6h-54-63=0

We multiply all the terms by the denominator


6h*2h-54*2h-63*2h+1=0

Wy multiply elements

12h^2-108h-126h+1=0

We add all the numbers together, and all the variables

12h^2-234h+1=0

a = 12; b = -234; c = +1;
Δ = b2-4ac
Δ = -2342-4·12·1
Δ = 54708
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:

$\sqrt{\Delta}=\sqrt{54708}=\sqrt{4*13677}=\sqrt{4}*\sqrt{13677}=2\sqrt{13677}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-2\sqrt{13677}}{2*12}=\frac{234-2\sqrt{13677}}{24}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+2\sqrt{13677}}{2*12}=\frac{234+2\sqrt{13677}}{24}
$