Y=2x^2-7x-72

Solution for Y=2x^2-7x-72 equation:

=2Y^2-7Y-72

We move all terms to the left:

-(2Y^2-7Y-72)=0

We get rid of parentheses

-2Y^2+7Y+72=0

a = -2; b = 7; c = +72;
Δ = b2-4ac
Δ = 72-4·(-2)·72
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*-2}=\frac{-32}{-4}
=+8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*-2}=\frac{18}{-4}
=-4+1/2
$