3x+24X^2+12X^2=528

Solution for 3x+24X^2+12X^2=528 equation:

3x+24x^2+12x^2=528

We move all terms to the left:

3x+24x^2+12x^2-(528)=0

We add all the numbers together, and all the variables

36x^2+3x-528=0

a = 36; b = 3; c = -528;
Δ = b2-4ac
Δ = 32-4·36·(-528)
Δ = 76041
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:

$\sqrt{\Delta}=\sqrt{76041}=\sqrt{9*8449}=\sqrt{9}*\sqrt{8449}=3\sqrt{8449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{8449}}{2*36}=\frac{-3-3\sqrt{8449}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{8449}}{2*36}=\frac{-3+3\sqrt{8449}}{72}
$