42x=-3x^2-144

Solution for 42x=-3x^2-144 equation:

42x=-3x^2-144

We move all terms to the left:

42x-(-3x^2-144)=0

We get rid of parentheses

3x^2+42x+144=0

a = 3; b = 42; c = +144;
Δ = b2-4ac
Δ = 422-4·3·144
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6}{2*3}=\frac{-36}{6}
=-6
$