3h=6(h-1)9h-6

Solution for 3h=6(h-1)9h-6 equation:

3h=6(h-1)9h-6

We move all terms to the left:

3h-(6(h-1)9h-6)=0


We calculate terms in parentheses: -(6(h-1)9h-6), so:

6(h-1)9h-6

We multiply parentheses

54h^2-54h-6

Back to the equation:

-(54h^2-54h-6)


We get rid of parentheses

-54h^2+3h+54h+6=0

We add all the numbers together, and all the variables

-54h^2+57h+6=0

a = -54; b = 57; c = +6;
Δ = b2-4ac
Δ = 572-4·(-54)·6
Δ = 4545
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:

$\sqrt{\Delta}=\sqrt{4545}=\sqrt{9*505}=\sqrt{9}*\sqrt{505}=3\sqrt{505}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{505}}{2*-54}=\frac{-57-3\sqrt{505}}{-108}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{505}}{2*-54}=\frac{-57+3\sqrt{505}}{-108}
$