2x(3x-7)=22

Solution for 2x(3x-7)=22 equation:

2x(3x-7)=22

We move all terms to the left:

2x(3x-7)-(22)=0

We multiply parentheses

6x^2-14x-22=0

a = 6; b = -14; c = -22;
Δ = b2-4ac
Δ = -142-4·6·(-22)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{181}}{2*6}=\frac{14-2\sqrt{181}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{181}}{2*6}=\frac{14+2\sqrt{181}}{12}
$