4(2x-11)6x=-3

Solution for 4(2x-11)6x=-3 equation:

4(2x-11)6x=-3

We move all terms to the left:

4(2x-11)6x-(-3)=0

We add all the numbers together, and all the variables

4(2x-11)6x+3=0

We multiply parentheses

48x^2-264x+3=0

a = 48; b = -264; c = +3;
Δ = b2-4ac
Δ = -2642-4·48·3
Δ = 69120
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:

$\sqrt{\Delta}=\sqrt{69120}=\sqrt{2304*30}=\sqrt{2304}*\sqrt{30}=48\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-48\sqrt{30}}{2*48}=\frac{264-48\sqrt{30}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+48\sqrt{30}}{2*48}=\frac{264+48\sqrt{30}}{96}
$