H=5t^2-7t+2

Solution for H=5t^2-7t+2 equation:

=5H^2-7H+2

We move all terms to the left:

-(5H^2-7H+2)=0

We get rid of parentheses

-5H^2+7H-2=0

a = -5; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-5)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-5}=\frac{-10}{-10}
=1
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-5}=\frac{-4}{-10}
=2/5
$