(3x-11)(8x-4)=5

Solution for (3x-11)(8x-4)=5 equation:

(3x-11)(8x-4)=5

We move all terms to the left:

(3x-11)(8x-4)-(5)=0

We multiply parentheses ..

(+24x^2-12x-88x+44)-5=0

We get rid of parentheses

24x^2-12x-88x+44-5=0

We add all the numbers together, and all the variables

24x^2-100x+39=0

a = 24; b = -100; c = +39;
Δ = b2-4ac
Δ = -1002-4·24·39
Δ = 6256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6256}=\sqrt{16*391}=\sqrt{16}*\sqrt{391}=4\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{391}}{2*24}=\frac{100-4\sqrt{391}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{391}}{2*24}=\frac{100+4\sqrt{391}}{48}
$