6x2+2x=50

Solution for 6x2+2x=50 equation:

6x^2+2x=50

We move all terms to the left:

6x^2+2x-(50)=0

a = 6; b = 2; c = -50;
Δ = b2-4ac
Δ = 22-4·6·(-50)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{301}}{2*6}=\frac{-2-2\sqrt{301}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{301}}{2*6}=\frac{-2+2\sqrt{301}}{12}
$