7+6(-8-3h)h=9

Solution for 7+6(-8-3h)h=9 equation:

7+6(-8-3h)h=9

We move all terms to the left:

7+6(-8-3h)h-(9)=0

We add all the numbers together, and all the variables

6(-3h-8)h+7-9=0

We add all the numbers together, and all the variables

6(-3h-8)h-2=0

We multiply parentheses

-18h^2-48h-2=0

a = -18; b = -48; c = -2;
Δ = b2-4ac
Δ = -482-4·(-18)·(-2)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{15}}{2*-18}=\frac{48-12\sqrt{15}}{-36}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{15}}{2*-18}=\frac{48+12\sqrt{15}}{-36}
$