H=70-10x-5x^2

Solution for H=70-10x-5x^2 equation:

=70-10H-5H^2

We move all terms to the left:

-(70-10H-5H^2)=0

We get rid of parentheses

5H^2+10H-70=0

a = 5; b = 10; c = -70;
Δ = b2-4ac
Δ = 102-4·5·(-70)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{15}}{2*5}=\frac{-10-10\sqrt{15}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{15}}{2*5}=\frac{-10+10\sqrt{15}}{10}
$