Y=5x2-53x-22

Solution for Y=5x2-53x-22 equation:

=5Y^2-53Y-22

We move all terms to the left:

-(5Y^2-53Y-22)=0

We get rid of parentheses

-5Y^2+53Y+22=0

a = -5; b = 53; c = +22;
Δ = b2-4ac
Δ = 532-4·(-5)·22
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-57}{2*-5}=\frac{-110}{-10}
=+11
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+57}{2*-5}=\frac{4}{-10}
=-2/5
$