H=-t*t+3t+10

Solution for H=-t*t+3t+10 equation:

=-H*H+3H+10

We move all terms to the left:

-(-H*H+3H+10)=0

We add all the numbers together, and all the variables

-(3H-H*H+10)=0

We get rid of parentheses

-3H+H*H-10=0

Wy multiply elements

H^2-3H-10=0

a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2}
=-2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2}
=5
$