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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x^2-2x-30x-(x+2x(x-11))+8=0


We calculate terms in parentheses: -(x+2x(x-11)), so:

x+2x(x-11)

We multiply parentheses

2x^2+x-22x

We add all the numbers together, and all the variables

2x^2-21x

Back to the equation:

-(2x^2-21x)


We add all the numbers together, and all the variables

5x^2-32x-(2x^2-21x)+8=0

We get rid of parentheses

5x^2-2x^2-32x+21x+8=0

We add all the numbers together, and all the variables

3x^2-11x+8=0

a = 3; b = -11; c = +8;
Δ = b2-4ac
Δ = -112-4·3·8
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*3}=\frac{16}{6}
=2+2/3
$