Y=5x^2-19x-30

Solution for Y=5x^2-19x-30 equation:

=5Y^2-19Y-30

We move all terms to the left:

-(5Y^2-19Y-30)=0

We get rid of parentheses

-5Y^2+19Y+30=0

a = -5; b = 19; c = +30;
Δ = b2-4ac
Δ = 192-4·(-5)·30
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-31}{2*-5}=\frac{-50}{-10}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+31}{2*-5}=\frac{12}{-10}
=-1+1/5
$