(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+19x-77=0

a = 6; b = 19; c = -77;
Δ = b2-4ac
Δ = 192-4·6·(-77)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-47}{2*6}=\frac{-66}{12}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+47}{2*6}=\frac{28}{12}
=2+1/3
$