3(h-6)=2(5-2h)3h

Solution for 3(h-6)=2(5-2h)3h equation:

3(h-6)=2(5-2h)3h

We move all terms to the left:

3(h-6)-(2(5-2h)3h)=0

We add all the numbers together, and all the variables

3(h-6)-(2(-2h+5)3h)=0

We multiply parentheses

3h-(2(-2h+5)3h)-18=0


We calculate terms in parentheses: -(2(-2h+5)3h), so:

2(-2h+5)3h

We multiply parentheses

-12h^2+30h

Back to the equation:

-(-12h^2+30h)


We get rid of parentheses

12h^2-30h+3h-18=0

We add all the numbers together, and all the variables

12h^2-27h-18=0

a = 12; b = -27; c = -18;
Δ = b2-4ac
Δ = -272-4·12·(-18)
Δ = 1593
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:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{177}}{2*12}=\frac{27-3\sqrt{177}}{24}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{177}}{2*12}=\frac{27+3\sqrt{177}}{24}
$