3x(4-2x)-(5+x)=0

Solution for 3x(4-2x)-(5+x)=0 equation:

3x(4-2x)-(5+x)=0

We add all the numbers together, and all the variables

3x(-2x+4)-(x+5)=0

We multiply parentheses

-6x^2+12x-(x+5)=0

We get rid of parentheses

-6x^2+12x-x-5=0

We add all the numbers together, and all the variables

-6x^2+11x-5=0

a = -6; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-6)·(-5)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*-6}=\frac{-10}{-12}
=5/6
$