Y=X2+4x-45

Solution for Y=X2+4x-45 equation:

=Y2+4Y-45

We move all terms to the left:

-(Y2+4Y-45)=0

We add all the numbers together, and all the variables

-(+Y^2+4Y-45)=0

We get rid of parentheses

-Y^2-4Y+45=0

We add all the numbers together, and all the variables

-1Y^2-4Y+45=0

a = -1; b = -4; c = +45;
Δ = b2-4ac
Δ = -42-4·(-1)·45
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*-1}=\frac{-10}{-2}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*-1}=\frac{18}{-2}
=-9
$