Equation problem?

Question

How to factor an 'S' from this equation?
L=(S² A)/(200 (H + S tanQ)
I need to find an 'S' if 'L' is given.

Actually the equation is used to find the minimum length (L) of sag vertical curve for given sight distance (S) in road design and I usually design the road using specific length of the curve. So i need the equation to find the sight distance of the curve using other than trial and error, back calculation etc...

Answer 1

L = S^2A / [200(H + StanQ)]

Multiply both sides by 200(H + StanQ) :
200L(H + StanQ) = S^2A

Expand the left-hand side :
200LH + 200LStanQ = S^2A

Rewrite it as a standard quadratic in S :
(A)S^2 - (200LtanQ)S - 200LH = 0

Use the quadratic formula :
S = {200LtanQ ± sqrt[40000L^2tan^2Q + 4A(200LH)]} / (2A)

= (10 / A) * {10LtanQ ± sqrt[2L(50Ltan^2Q + AH)]}

Answer 2

This equation can be rearranged into a standard quadratic equation.

You have not written your equation correctly (there is a bracket missing somewhere). I am going to assume you meant the following:

L = (S^2A)/(200*(H+StanQ))
S^2A = L200(H+StanQ)
S^2A = 200LH + 200LStanQ
can be rearranged to:
(A)*S^2 - (200 L tanQ)*S - 200LH = 0

This is in the form
aS^2 + bS + c = 0 and the quadratic formula can be used to solve. :)

Answer 3

L=(S² A) / (200 (H + S tanQ))
L(200 (H + S tanQ)) = (S² A)
200L (H + S tanQ) = A S²
200LH + 200L(tanQ))S = A S²
A S² - 200L(tanQ))S - 200LH = 0

You now have a quadratic for S. You can use the quadratic forumula to solve it. Then simplify.

S = [200L(tanQ) ±√[ 40000L²(tan²Q) - 4(A)(-200LH) ]] / 2A
S = [100L(tanQ) ±√[ 10000L²(tan²Q) - (A)(-200LH) ]] / A
S = [100L(tanQ) ±√[ 10000L²(tan²Q) + 200ALH ]] / A
S = [100L(tanQ) ± 10√[100L²(tan²Q) + 2ALH] ] / A

Answer 4

L=(S² A)/(200 (H + S tanQ)
200 (H + S tanQ)L=(S² A)
(200H + 200S tanQ)L= S² A
200(HL) + 200L tanQ(S) = S² A
AS² - 200L tanQ(S) - 200(HL)= 0
Now you have a quadratic equation.
Quatratic equation formula :
[-b ± √(b)² - 4.a.c)] / 2a
and
a = A
b = - 200L tanQ
c = - 200(HL)

[-b ± √(b)² - 4.a.c)] / 2a
[-( - 200L tanQ) ± √[( - 200L tanQ)² - 4*A*- 200(HL)]] / 2(A)
[200L tanQ ± √[( - 200L tanQ)² + 800AHL)]] / 2(A)
[200L tanQ ± √[( - 200L tanQ)² + 800AHL)] / 2(A)
[200L tanQ ± √[(40,000L² (tanQ)² + 800AHL)]] / 2(A)

This is about as far as I can take it without more information.
You need values for Q, A, H and L.

Answer 5

200 L.(H + S tan Q) = S²A
200L.H + 200.L.S.tan Q = S².A
200L.H = S².A - 200.L.S.tanQ
A.S² - (200.L.tanQ).S - 200.L.H = 0
S can be found from this equation if values for A,Q,L and H are known.