(6x-1)(11x+4)=75

Solution for (6x-1)(11x+4)=75 equation:

(6x-1)(11x+4)=75

We move all terms to the left:

(6x-1)(11x+4)-(75)=0

We multiply parentheses ..

(+66x^2+24x-11x-4)-75=0

We get rid of parentheses

66x^2+24x-11x-4-75=0

We add all the numbers together, and all the variables

66x^2+13x-79=0

a = 66; b = 13; c = -79;
Δ = b2-4ac
Δ = 132-4·66·(-79)
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-145}{2*66}=\frac{-158}{132}
=-1+13/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+145}{2*66}=\frac{132}{132}
=1
$