Y=5x2-44x+91

Solution for Y=5x2-44x+91 equation:

=5Y^2-44Y+91

We move all terms to the left:

-(5Y^2-44Y+91)=0

We get rid of parentheses

-5Y^2+44Y-91=0

a = -5; b = 44; c = -91;
Δ = b2-4ac
Δ = 442-4·(-5)·(-91)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{29}}{2*-5}=\frac{-44-2\sqrt{29}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{29}}{2*-5}=\frac{-44+2\sqrt{29}}{-10}
$