14x(6x+14)=194

Solution for 14x(6x+14)=194 equation:

14x(6x+14)=194

We move all terms to the left:

14x(6x+14)-(194)=0

We multiply parentheses

84x^2+196x-194=0

a = 84; b = 196; c = -194;
Δ = b2-4ac
Δ = 1962-4·84·(-194)
Δ = 103600
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:

$\sqrt{\Delta}=\sqrt{103600}=\sqrt{400*259}=\sqrt{400}*\sqrt{259}=20\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-20\sqrt{259}}{2*84}=\frac{-196-20\sqrt{259}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+20\sqrt{259}}{2*84}=\frac{-196+20\sqrt{259}}{168}
$