2x(3x+14)=109

Solution for 2x(3x+14)=109 equation:

2x(3x+14)=109

We move all terms to the left:

2x(3x+14)-(109)=0

We multiply parentheses

6x^2+28x-109=0

a = 6; b = 28; c = -109;
Δ = b2-4ac
Δ = 282-4·6·(-109)
Δ = 3400
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:

$\sqrt{\Delta}=\sqrt{3400}=\sqrt{100*34}=\sqrt{100}*\sqrt{34}=10\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-10\sqrt{34}}{2*6}=\frac{-28-10\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+10\sqrt{34}}{2*6}=\frac{-28+10\sqrt{34}}{12}
$