(6x-11)(2x+5)=0

Solution for (6x-11)(2x+5)=0 equation:

(6x-11)(2x+5)=0

We multiply parentheses ..

(+12x^2+30x-22x-55)=0

We get rid of parentheses

12x^2+30x-22x-55=0

We add all the numbers together, and all the variables

12x^2+8x-55=0

a = 12; b = 8; c = -55;
Δ = b2-4ac
Δ = 82-4·12·(-55)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-52}{2*12}=\frac{-60}{24}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+52}{2*12}=\frac{44}{24}
=1+5/6
$