6x^2+62x=14

Solution for 6x^2+62x=14 equation:

6x^2+62x=14

We move all terms to the left:

6x^2+62x-(14)=0

a = 6; b = 62; c = -14;
Δ = b2-4ac
Δ = 622-4·6·(-14)
Δ = 4180
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:

$\sqrt{\Delta}=\sqrt{4180}=\sqrt{4*1045}=\sqrt{4}*\sqrt{1045}=2\sqrt{1045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1045}}{2*6}=\frac{-62-2\sqrt{1045}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1045}}{2*6}=\frac{-62+2\sqrt{1045}}{12}
$