42x=-99-3x^2

Solution for 42x=-99-3x^2 equation:

42x=-99-3x^2

We move all terms to the left:

42x-(-99-3x^2)=0

We get rid of parentheses

3x^2+42x+99=0

a = 3; b = 42; c = +99;
Δ = b2-4ac
Δ = 422-4·3·99
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-24}{2*3}=\frac{-66}{6}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+24}{2*3}=\frac{-18}{6}
=-3
$