Y=0.5(x+4)(x-3)

Solution for Y=0.5(x+4)(x-3) equation:

=0.5(Y+4)(Y-3)

We move all terms to the left:

-(0.5(Y+4)(Y-3))=0

We multiply parentheses ..

-(0.5(+Y^2-3Y+4Y-12))=0


We calculate terms in parentheses: -(0.5(+Y^2-3Y+4Y-12)), so:

0.5(+Y^2-3Y+4Y-12)

We multiply parentheses

0.5Y^2-1.5Y+2Y-6

We add all the numbers together, and all the variables

0.5Y^2+0.5Y-6

Back to the equation:

-(0.5Y^2+0.5Y-6)


We get rid of parentheses

-0.5Y^2-0.5Y+6=0

a = -0.5; b = -0.5; c = +6;
Δ = b2-4ac
Δ = -0.52-4·(-0.5)·6
Δ = 12.25
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{-(-0.5)-\sqrt{12.25}}{2*-0.5}=\frac{0.5-\sqrt{12.25}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{12.25}}{2*-0.5}=\frac{0.5+\sqrt{12.25}}{-1}
$