3x+9x^2-27=-21x^2

Solution for 3x+9x^2-27=-21x^2 equation:

3x+9x^2-27=-21x^2

We move all terms to the left:

3x+9x^2-27-(-21x^2)=0

We get rid of parentheses

9x^2+21x^2+3x-27=0

We add all the numbers together, and all the variables

30x^2+3x-27=0

a = 30; b = 3; c = -27;
Δ = b2-4ac
Δ = 32-4·30·(-27)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-57}{2*30}=\frac{-60}{60}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+57}{2*30}=\frac{54}{60}
=9/10
$