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

Solution for 11x-(2x+1)(7x-6)=0 equation:

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

We multiply parentheses ..

-(+14x^2-12x+7x-6)+11x=0

We get rid of parentheses

-14x^2+12x-7x+11x+6=0

We add all the numbers together, and all the variables

-14x^2+16x+6=0

a = -14; b = 16; c = +6;
Δ = b2-4ac
Δ = 162-4·(-14)·6
Δ = 592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{37}}{2*-14}=\frac{-16-4\sqrt{37}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{37}}{2*-14}=\frac{-16+4\sqrt{37}}{-28}
$