4x(3x+7)-8x(2x-4)=0)

Solution for 4x(3x+7)-8x(2x-4)=0) equation:

4x(3x+7)-8x(2x-4)=0)

We move all terms to the left:

4x(3x+7)-8x(2x-4)-(0))=0

We add all the numbers together, and all the variables

4x(3x+7)-8x(2x-4)=0

We multiply parentheses

12x^2-16x^2+28x+32x=0

We add all the numbers together, and all the variables

-4x^2+60x=0

a = -4; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-4)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-4}=\frac{-120}{-8}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-4}=\frac{0}{-8}
=0
$