3x(x-6)+2x=22

Solution for 3x(x-6)+2x=22 equation:

3x(x-6)+2x=22

We move all terms to the left:

3x(x-6)+2x-(22)=0

We add all the numbers together, and all the variables

2x+3x(x-6)-22=0

We multiply parentheses

3x^2+2x-18x-22=0

We add all the numbers together, and all the variables

3x^2-16x-22=0

a = 3; b = -16; c = -22;
Δ = b2-4ac
Δ = -162-4·3·(-22)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{130}}{2*3}=\frac{16-2\sqrt{130}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{130}}{2*3}=\frac{16+2\sqrt{130}}{6}
$