(3x-7)(2x-11)=0

Solution for (3x-7)(2x-11)=0 equation:

(3x-7)(2x-11)=0

We multiply parentheses ..

(+6x^2-33x-14x+77)=0

We get rid of parentheses

6x^2-33x-14x+77=0

We add all the numbers together, and all the variables

6x^2-47x+77=0

a = 6; b = -47; c = +77;
Δ = b2-4ac
Δ = -472-4·6·77
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-19}{2*6}=\frac{28}{12}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+19}{2*6}=\frac{66}{12}
=5+1/2
$