(11-3x)(3x-7)=0

Solution for (11-3x)(3x-7)=0 equation:

(11-3x)(3x-7)=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-9x^2+21x+33x-77)=0

We get rid of parentheses

-9x^2+21x+33x-77=0

We add all the numbers together, and all the variables

-9x^2+54x-77=0

a = -9; b = 54; c = -77;
Δ = b2-4ac
Δ = 542-4·(-9)·(-77)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-12}{2*-9}=\frac{-66}{-18}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+12}{2*-9}=\frac{-42}{-18}
=2+1/3
$