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

Solution for (2x-6)(-3x+11)=0 equation:

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

We multiply parentheses ..

(-6x^2+22x+18x-66)=0

We get rid of parentheses

-6x^2+22x+18x-66=0

We add all the numbers together, and all the variables

-6x^2+40x-66=0

a = -6; b = 40; c = -66;
Δ = b2-4ac
Δ = 402-4·(-6)·(-66)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4}{2*-6}=\frac{-44}{-12}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4}{2*-6}=\frac{-36}{-12}
=+3
$