Y=x2-41/5

Solution for Y=x2-41/5 equation:

=Y2-41/5

We move all terms to the left:

-(Y2-41/5)=0

We add all the numbers together, and all the variables

-(+Y^2-41/5)=0

We get rid of parentheses

-Y^2+41/5=0

We multiply all the terms by the denominator


-Y^2*5+41=0

Wy multiply elements

-5Y^2+41=0

a = -5; b = 0; c = +41;
Δ = b2-4ac
Δ = 02-4·(-5)·41
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{205}}{2*-5}=\frac{0-2\sqrt{205}}{-10}
=-\frac{2\sqrt{205}}{-10}
=-\frac{\sqrt{205}}{-5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{205}}{2*-5}=\frac{0+2\sqrt{205}}{-10}
=\frac{2\sqrt{205}}{-10}
=\frac{\sqrt{205}}{-5}
$