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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-12x^2+66x+5=0

a = -12; b = 66; c = +5;
Δ = b2-4ac
Δ = 662-4·(-12)·5
Δ = 4596
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:

$\sqrt{\Delta}=\sqrt{4596}=\sqrt{4*1149}=\sqrt{4}*\sqrt{1149}=2\sqrt{1149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1149}}{2*-12}=\frac{-66-2\sqrt{1149}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1149}}{2*-12}=\frac{-66+2\sqrt{1149}}{-24}
$