Y=x2+4x+3

Solution for Y=x2+4x+3 equation:

=Y2+4Y+3

We move all terms to the left:

-(Y2+4Y+3)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-Y^2-4Y-3=0

We add all the numbers together, and all the variables

-1Y^2-4Y-3=0

a = -1; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·(-1)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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