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

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

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

We multiply parentheses ..

(+2x^2-11x+12x-66)=0

We get rid of parentheses

2x^2-11x+12x-66=0

We add all the numbers together, and all the variables

2x^2+x-66=0

a = 2; b = 1; c = -66;
Δ = b2-4ac
Δ = 12-4·2·(-66)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-23}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+23}{2*2}=\frac{22}{4}
=5+1/2
$