(5x+11)(6x-3)=0

Solution for (5x+11)(6x-3)=0 equation:

(5x+11)(6x-3)=0

We multiply parentheses ..

(+30x^2-15x+66x-33)=0

We get rid of parentheses

30x^2-15x+66x-33=0

We add all the numbers together, and all the variables

30x^2+51x-33=0

a = 30; b = 51; c = -33;
Δ = b2-4ac
Δ = 512-4·30·(-33)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-81}{2*30}=\frac{-132}{60}
=-2+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+81}{2*30}=\frac{30}{60}
=1/2
$