7(h)=(1/3)(h+2)

Solution for 7(h)=(1/3)(h+2) equation:

7(h)=(1/3)(h+2)

We move all terms to the left:

7(h)-((1/3)(h+2))=0


Domain of the equation: 3)(h+2))!=0

h∈R


We add all the numbers together, and all the variables

7h-((+1/3)(h+2))=0

We multiply parentheses ..

-((+h^2+1/3*2))+7h=0

We multiply all the terms by the denominator


-((+h^2+1+7h*3*2))=0


We calculate terms in parentheses: -((+h^2+1+7h*3*2)), so:

(+h^2+1+7h*3*2)

We get rid of parentheses

h^2+7h*3*2+1

Wy multiply elements

h^2+42h*2+1

Wy multiply elements

h^2+84h+1

Back to the equation:

-(h^2+84h+1)


We get rid of parentheses

-h^2-84h-1=0

We add all the numbers together, and all the variables

-1h^2-84h-1=0

a = -1; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·(-1)·(-1)
Δ = 7052
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:

$\sqrt{\Delta}=\sqrt{7052}=\sqrt{4*1763}=\sqrt{4}*\sqrt{1763}=2\sqrt{1763}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1763}}{2*-1}=\frac{84-2\sqrt{1763}}{-2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1763}}{2*-1}=\frac{84+2\sqrt{1763}}{-2}
$