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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-12x-(-3x)=0

We get rid of parentheses

4x^2-12x+3x=0

We add all the numbers together, and all the variables

4x^2-9x=0

a = 4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·4·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*4}=\frac{18}{8}
=2+1/4
$