2(x+7)-34=4x-11x(x-1)

Solution for 2(x+7)-34=4x-11x(x-1) equation:

2(x+7)-34=4x-11x(x-1)

We move all terms to the left:

2(x+7)-34-(4x-11x(x-1))=0

We multiply parentheses

2x-(4x-11x(x-1))+14-34=0


We calculate terms in parentheses: -(4x-11x(x-1)), so:

4x-11x(x-1)

We multiply parentheses

-11x^2+4x+11x

We add all the numbers together, and all the variables

-11x^2+15x

Back to the equation:

-(-11x^2+15x)


We add all the numbers together, and all the variables

-(-11x^2+15x)+2x-20=0

We get rid of parentheses

11x^2-15x+2x-20=0

We add all the numbers together, and all the variables

11x^2-13x-20=0

a = 11; b = -13; c = -20;
Δ = b2-4ac
Δ = -132-4·11·(-20)
Δ = 1049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{1049}}{2*11}=\frac{13-\sqrt{1049}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1049}}{2*11}=\frac{13+\sqrt{1049}}{22}
$