10+h=1/3h+12

Solution for 10+h=1/3h+12 equation:

10+h=1/3h+12

We move all terms to the left:

10+h-(1/3h+12)=0


Domain of the equation: 3h+12)!=0

h∈R


We get rid of parentheses

h-1/3h-12+10=0

We multiply all the terms by the denominator


h*3h-12*3h+10*3h-1=0

Wy multiply elements

3h^2-36h+30h-1=0

We add all the numbers together, and all the variables

3h^2-6h-1=0

a = 3; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·3·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{3}}{2*3}=\frac{6-4\sqrt{3}}{6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{3}}{2*3}=\frac{6+4\sqrt{3}}{6}
$