x+6(x^2-7x+12)=22

Solution for x+6(x^2-7x+12)=22 equation:

x+6(x^2-7x+12)=22

We move all terms to the left:

x+6(x^2-7x+12)-(22)=0

We multiply parentheses

6x^2+x-42x+72-22=0

We add all the numbers together, and all the variables

6x^2-41x+50=0

a = 6; b = -41; c = +50;
Δ = b2-4ac
Δ = -412-4·6·50
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{481}}{2*6}=\frac{41-\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{481}}{2*6}=\frac{41+\sqrt{481}}{12}
$