h(h+6)=2(3h+27)

Solution for h(h+6)=2(3h+27) equation:

h(h+6)=2(3h+27)

We move all terms to the left:

h(h+6)-(2(3h+27))=0

We multiply parentheses

h^2+6h-(2(3h+27))=0


We calculate terms in parentheses: -(2(3h+27)), so:

2(3h+27)

We multiply parentheses

6h+54

Back to the equation:

-(6h+54)


We get rid of parentheses

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

We add all the numbers together, and all the variables

h^2-54=0

a = 1; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·1·(-54)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*1}=\frac{0-6\sqrt{6}}{2}
=-\frac{6\sqrt{6}}{2}
=-3\sqrt{6}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*1}=\frac{0+6\sqrt{6}}{2}
=\frac{6\sqrt{6}}{2}
=3\sqrt{6}
$