Y-12=x^2-7x

Solution for Y-12=x^2-7x equation:

-12=Y^2-7Y

We move all terms to the left:

-12-(Y^2-7Y)=0

We get rid of parentheses

-Y^2+7Y-12=0

We add all the numbers together, and all the variables

-1Y^2+7Y-12=0

a = -1; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·(-1)·(-12)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*-1}=\frac{-8}{-2}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-1}=\frac{-6}{-2}
=+3
$