2x^2+3x+12=507

Solution for 2x^2+3x+12=507 equation:

2x^2+3x+12=507

We move all terms to the left:

2x^2+3x+12-(507)=0

We add all the numbers together, and all the variables

2x^2+3x-495=0

a = 2; b = 3; c = -495;
Δ = b2-4ac
Δ = 32-4·2·(-495)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-63}{2*2}=\frac{-66}{4}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+63}{2*2}=\frac{60}{4}
=15
$