11-(3x+1)=7x(x-6+2)

Solution for 11-(3x+1)=7x(x-6+2) equation:

11-(3x+1)=7x(x-6+2)

We move all terms to the left:

11-(3x+1)-(7x(x-6+2))=0

We add all the numbers together, and all the variables

-(3x+1)-(7x(x-4))+11=0

We get rid of parentheses

-3x-(7x(x-4))-1+11=0


We calculate terms in parentheses: -(7x(x-4)), so:

7x(x-4)

We multiply parentheses

7x^2-28x

Back to the equation:

-(7x^2-28x)


We add all the numbers together, and all the variables

-3x-(7x^2-28x)+10=0

We get rid of parentheses

-7x^2-3x+28x+10=0

We add all the numbers together, and all the variables

-7x^2+25x+10=0

a = -7; b = 25; c = +10;
Δ = b2-4ac
Δ = 252-4·(-7)·10
Δ = 905
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{-(25)-\sqrt{905}}{2*-7}=\frac{-25-\sqrt{905}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{905}}{2*-7}=\frac{-25+\sqrt{905}}{-14}
$