3x2+51x=-216

Solution for 3x2+51x=-216 equation:

3x^2+51x=-216

We move all terms to the left:

3x^2+51x-(-216)=0

We add all the numbers together, and all the variables

3x^2+51x+216=0

a = 3; b = 51; c = +216;
Δ = b2-4ac
Δ = 512-4·3·216
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3}{2*3}=\frac{-48}{6}
=-8
$