3x^2+30x=-51

Solution for 3x^2+30x=-51 equation:

3x^2+30x=-51

We move all terms to the left:

3x^2+30x-(-51)=0

We add all the numbers together, and all the variables

3x^2+30x+51=0

a = 3; b = 30; c = +51;
Δ = b2-4ac
Δ = 302-4·3·51
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{2}}{2*3}=\frac{-30-12\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{2}}{2*3}=\frac{-30+12\sqrt{2}}{6}
$