3x(x+6)=2x-3

Solution for 3x(x+6)=2x-3 equation:

3x(x+6)=2x-3

We move all terms to the left:

3x(x+6)-(2x-3)=0

We multiply parentheses

3x^2+18x-(2x-3)=0

We get rid of parentheses

3x^2+18x-2x+3=0

We add all the numbers together, and all the variables

3x^2+16x+3=0

a = 3; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·3·3
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{55}}{2*3}=\frac{-16-2\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{55}}{2*3}=\frac{-16+2\sqrt{55}}{6}
$