3x(2x+3)=51

Solution for 3x(2x+3)=51 equation:

3x(2x+3)=51

We move all terms to the left:

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

We multiply parentheses

6x^2+9x-51=0

a = 6; b = 9; c = -51;
Δ = b2-4ac
Δ = 92-4·6·(-51)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{145}}{2*6}=\frac{-9-3\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{145}}{2*6}=\frac{-9+3\sqrt{145}}{12}
$