H=49-2x-5x^2

Solution for H=49-2x-5x^2 equation:

=49-2H-5H^2

We move all terms to the left:

-(49-2H-5H^2)=0

We get rid of parentheses

5H^2+2H-49=0

a = 5; b = 2; c = -49;
Δ = b2-4ac
Δ = 22-4·5·(-49)
Δ = 984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{246}}{2*5}=\frac{-2-2\sqrt{246}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{246}}{2*5}=\frac{-2+2\sqrt{246}}{10}
$