8(h-1)=1/2h-6

Solution for 8(h-1)=1/2h-6 equation:

8(h-1)=1/2h-6

We move all terms to the left:

8(h-1)-(1/2h-6)=0


Domain of the equation: 2h-6)!=0

h∈R


We multiply parentheses

8h-(1/2h-6)-8=0

We get rid of parentheses

8h-1/2h+6-8=0

We multiply all the terms by the denominator


8h*2h+6*2h-8*2h-1=0

Wy multiply elements

16h^2+12h-16h-1=0

We add all the numbers together, and all the variables

16h^2-4h-1=0

a = 16; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·16·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*16}=\frac{4-4\sqrt{5}}{32}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*16}=\frac{4+4\sqrt{5}}{32}
$