x^2=-3(3x+1)

Solution for x^2=-3(3x+1) equation:

x^2=-3(3x+1)

We move all terms to the left:

x^2-(-3(3x+1))=0


We calculate terms in parentheses: -(-3(3x+1)), so:

-3(3x+1)

We multiply parentheses

-9x-3

Back to the equation:

-(-9x-3)


We get rid of parentheses

x^2+9x+3=0

a = 1; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·1·3
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{69}}{2*1}=\frac{-9-\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{69}}{2*1}=\frac{-9+\sqrt{69}}{2}
$