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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-8x^2-7x-6x-4x=0

We add all the numbers together, and all the variables

-5x^2-17x=0

a = -5; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-5)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-5}=\frac{34}{-10}
=-3+2/5
$