3(h-4)=-(1/2)(24-6h)

Solution for 3(h-4)=-(1/2)(24-6h) equation:

3(h-4)=-(1/2)(24-6h)

We move all terms to the left:

3(h-4)-(-(1/2)(24-6h))=0


Domain of the equation: 2)(24-6h))!=0

h∈R


We add all the numbers together, and all the variables

3(h-4)-(-(+1/2)(-6h+24))=0

We multiply parentheses

3h-(-(+1/2)(-6h+24))-12=0

We multiply parentheses ..

-(-(-6h^2+1/2*24))+3h-12=0

We multiply all the terms by the denominator


-(-(-6h^2+1+3h*2*24))-12*2*24))=0


We calculate terms in parentheses: -(-(-6h^2+1+3h*2*24)), so:

-(-6h^2+1+3h*2*24)

We get rid of parentheses

6h^2-3h*2*24-1

Wy multiply elements

6h^2-144h*2-1

Wy multiply elements

6h^2-288h-1

Back to the equation:

-(6h^2-288h-1)


We add all the numbers together, and all the variables

-(6h^2-288h-1)=0

We get rid of parentheses

-6h^2+288h+1=0

a = -6; b = 288; c = +1;
Δ = b2-4ac
Δ = 2882-4·(-6)·1
Δ = 82968
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:

$\sqrt{\Delta}=\sqrt{82968}=\sqrt{4*20742}=\sqrt{4}*\sqrt{20742}=2\sqrt{20742}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-2\sqrt{20742}}{2*-6}=\frac{-288-2\sqrt{20742}}{-12}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+2\sqrt{20742}}{2*-6}=\frac{-288+2\sqrt{20742}}{-12}
$