Y=(x*x)-6x-3

Solution for Y=(x*x)-6x-3 equation:

=(Y*Y)-6Y-3

We move all terms to the left:

-((Y*Y)-6Y-3)=0

We add all the numbers together, and all the variables

-((+Y*Y)-6Y-3)=0


We calculate terms in parentheses: -((+Y*Y)-6Y-3), so:

(+Y*Y)-6Y-3

We add all the numbers together, and all the variables

-6Y+(+Y*Y)-3

We get rid of parentheses

-6Y+Y*Y-3

Wy multiply elements

Y^2-6Y-3

Back to the equation:

-(Y^2-6Y-3)


We get rid of parentheses

-Y^2+6Y+3=0

We add all the numbers together, and all the variables

-1Y^2+6Y+3=0

a = -1; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-1)·3
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*-1}=\frac{-6-4\sqrt{3}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*-1}=\frac{-6+4\sqrt{3}}{-2}
$