Y=x^2+3x-12

Solution for Y=x^2+3x-12 equation:

=Y^2+3Y-12

We move all terms to the left:

-(Y^2+3Y-12)=0

We get rid of parentheses

-Y^2-3Y+12=0

We add all the numbers together, and all the variables

-1Y^2-3Y+12=0

a = -1; b = -3; c = +12;
Δ = b2-4ac
Δ = -32-4·(-1)·12
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{57}}{2*-1}=\frac{3-\sqrt{57}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*-1}=\frac{3+\sqrt{57}}{-2}
$