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

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

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

We multiply parentheses ..

(+30x^2+55x-18x-33)=0

We get rid of parentheses

30x^2+55x-18x-33=0

We add all the numbers together, and all the variables

30x^2+37x-33=0

a = 30; b = 37; c = -33;
Δ = b2-4ac
Δ = 372-4·30·(-33)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-73}{2*30}=\frac{-110}{60}
=-1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+73}{2*30}=\frac{36}{60}
=3/5
$