6(x-1)(3x+11)=-7

Solution for 6(x-1)(3x+11)=-7 equation:

6(x-1)(3x+11)=-7

We move all terms to the left:

6(x-1)(3x+11)-(-7)=0

We add all the numbers together, and all the variables

6(x-1)(3x+11)+7=0

We multiply parentheses ..

6(+3x^2+11x-3x-11)+7=0

We multiply parentheses

18x^2+66x-18x-66+7=0

We add all the numbers together, and all the variables

18x^2+48x-59=0

a = 18; b = 48; c = -59;
Δ = b2-4ac
Δ = 482-4·18·(-59)
Δ = 6552
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:

$\sqrt{\Delta}=\sqrt{6552}=\sqrt{36*182}=\sqrt{36}*\sqrt{182}=6\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{182}}{2*18}=\frac{-48-6\sqrt{182}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{182}}{2*18}=\frac{-48+6\sqrt{182}}{36}
$