P=8t^2+7t-9

Solution for P=8t^2+7t-9 equation:

=8P^2+7P-9

We move all terms to the left:

-(8P^2+7P-9)=0

We get rid of parentheses

-8P^2-7P+9=0

a = -8; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·(-8)·9
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{337}}{2*-8}=\frac{7-\sqrt{337}}{-16}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{337}}{2*-8}=\frac{7+\sqrt{337}}{-16}
$