H=3+75t-16(t*t)

Solution for H=3+75t-16(t*t) equation:

=3+75H-16(H*H)

We move all terms to the left:

-(3+75H-16(H*H))=0

We add all the numbers together, and all the variables

-(3+75H-16(+H*H))=0


We calculate terms in parentheses: -(3+75H-16(+H*H)), so:

3+75H-16(+H*H)

determiningTheFunctionDomain
75H-16(+H*H)+3

We multiply parentheses

-16H^2+75H+3

Back to the equation:

-(-16H^2+75H+3)


We get rid of parentheses

16H^2-75H-3=0

a = 16; b = -75; c = -3;
Δ = b2-4ac
Δ = -752-4·16·(-3)
Δ = 5817
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{-(-75)-\sqrt{5817}}{2*16}=\frac{75-\sqrt{5817}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5817}}{2*16}=\frac{75+\sqrt{5817}}{32}
$