30=12h(h+h+7)

Solution for 30=12h(h+h+7) equation:

30=12h(h+h+7)

We move all terms to the left:

30-(12h(h+h+7))=0

We add all the numbers together, and all the variables

-(12h(2h+7))+30=0


We calculate terms in parentheses: -(12h(2h+7)), so:

12h(2h+7)

We multiply parentheses

24h^2+84h

Back to the equation:

-(24h^2+84h)


We get rid of parentheses

-24h^2-84h+30=0

a = -24; b = -84; c = +30;
Δ = b2-4ac
Δ = -842-4·(-24)·30
Δ = 9936
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:

$\sqrt{\Delta}=\sqrt{9936}=\sqrt{144*69}=\sqrt{144}*\sqrt{69}=12\sqrt{69}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{69}}{2*-24}=\frac{84-12\sqrt{69}}{-48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{69}}{2*-24}=\frac{84+12\sqrt{69}}{-48}
$