4x(11-5x)=3(8x-2)+6

Solution for 4x(11-5x)=3(8x-2)+6 equation:

4x(11-5x)=3(8x-2)+6

We move all terms to the left:

4x(11-5x)-(3(8x-2)+6)=0

We add all the numbers together, and all the variables

4x(-5x+11)-(3(8x-2)+6)=0

We multiply parentheses

-20x^2+44x-(3(8x-2)+6)=0


We calculate terms in parentheses: -(3(8x-2)+6), so:

3(8x-2)+6

We multiply parentheses

24x-6+6

We add all the numbers together, and all the variables

24x

Back to the equation:

-(24x)


We add all the numbers together, and all the variables

-20x^2+20x=0

a = -20; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-20)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-20}=\frac{-40}{-40}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-20}=\frac{0}{-40}
=0
$