2x(3-x)-7x(3x+2)+4(2x+1)=0

Solution for 2x(3-x)-7x(3x+2)+4(2x+1)=0 equation:

2x(3-x)-7x(3x+2)+4(2x+1)=0

We add all the numbers together, and all the variables

2x(-1x+3)-7x(3x+2)+4(2x+1)=0

We multiply parentheses

-2x^2-21x^2+6x-14x+8x+4=0

We add all the numbers together, and all the variables

-23x^2+4=0

a = -23; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-23)·4
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{23}}{2*-23}=\frac{0-4\sqrt{23}}{-46}
=-\frac{4\sqrt{23}}{-46}
=-\frac{2\sqrt{23}}{-23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{23}}{2*-23}=\frac{0+4\sqrt{23}}{-46}
=\frac{4\sqrt{23}}{-46}
=\frac{2\sqrt{23}}{-23}
$