Y+18=x(x-3)

Solution for Y+18=x(x-3) equation:

+18=Y(Y-3)

We move all terms to the left:

+18-(Y(Y-3))=0


We calculate terms in parentheses: -(Y(Y-3)), so:

Y(Y-3)

We multiply parentheses

Y^2-3Y

Back to the equation:

-(Y^2-3Y)


We get rid of parentheses

-Y^2+3Y+18=0

We add all the numbers together, and all the variables

-1Y^2+3Y+18=0

a = -1; b = 3; c = +18;
Δ = b2-4ac
Δ = 32-4·(-1)·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-1}=\frac{-12}{-2}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-1}=\frac{6}{-2}
=-3
$