7-9(3x+1)=-27x2

Solution for 7-9(3x+1)=-27x2 equation:

7-9(3x+1)=-27x^2

We move all terms to the left:

7-9(3x+1)-(-27x^2)=0

We multiply parentheses

-(-27x^2)-27x-9+7=0

We get rid of parentheses

27x^2-27x-9+7=0

We add all the numbers together, and all the variables

27x^2-27x-2=0

a = 27; b = -27; c = -2;
Δ = b2-4ac
Δ = -272-4·27·(-2)
Δ = 945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{105}}{2*27}=\frac{27-3\sqrt{105}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{105}}{2*27}=\frac{27+3\sqrt{105}}{54}
$