3x^2+18x+144=381

Solution for 3x^2+18x+144=381 equation:

3x^2+18x+144=381

We move all terms to the left:

3x^2+18x+144-(381)=0

We add all the numbers together, and all the variables

3x^2+18x-237=0

a = 3; b = 18; c = -237;
Δ = b2-4ac
Δ = 182-4·3·(-237)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{22}}{2*3}=\frac{-18-12\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{22}}{2*3}=\frac{-18+12\sqrt{22}}{6}
$