38.5=(h+3)(h)

Solution for 38.5=(h+3)(h) equation:

38.5=(h+3)(h)

We move all terms to the left:

38.5-((h+3)(h))=0


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

(h+3)h

We multiply parentheses

h^2+3h

Back to the equation:

-(h^2+3h)


We get rid of parentheses

-h^2-3h+38.5=0

We add all the numbers together, and all the variables

-1h^2-3h+38.5=0

a = -1; b = -3; c = +38.5;
Δ = b2-4ac
Δ = -32-4·(-1)·38.5
Δ = 163
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{163}}{2*-1}=\frac{3-\sqrt{163}}{-2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{163}}{2*-1}=\frac{3+\sqrt{163}}{-2}
$