6x^2-196x=40

Solution for 6x^2-196x=40 equation:

6x^2-196x=40

We move all terms to the left:

6x^2-196x-(40)=0

a = 6; b = -196; c = -40;
Δ = b2-4ac
Δ = -1962-4·6·(-40)
Δ = 39376
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:

$\sqrt{\Delta}=\sqrt{39376}=\sqrt{16*2461}=\sqrt{16}*\sqrt{2461}=4\sqrt{2461}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-4\sqrt{2461}}{2*6}=\frac{196-4\sqrt{2461}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+4\sqrt{2461}}{2*6}=\frac{196+4\sqrt{2461}}{12}
$