11x-7x(x-4)=0

Solution for 11x-7x(x-4)=0 equation:

11x-7x(x-4)=0

We multiply parentheses

-7x^2+11x+28x=0

We add all the numbers together, and all the variables

-7x^2+39x=0

a = -7; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-7)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-7}=\frac{-78}{-14}
=5+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-7}=\frac{0}{-14}
=0
$