20x^2=196x-5=0

Solution for 20x^2=196x-5=0 equation:

20x^2=196x-5=0

We move all terms to the left:

20x^2-(196x-5)=0

We get rid of parentheses

20x^2-196x+5=0

a = 20; b = -196; c = +5;
Δ = b2-4ac
Δ = -1962-4·20·5
Δ = 38016
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:

$\sqrt{\Delta}=\sqrt{38016}=\sqrt{576*66}=\sqrt{576}*\sqrt{66}=24\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-24\sqrt{66}}{2*20}=\frac{196-24\sqrt{66}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+24\sqrt{66}}{2*20}=\frac{196+24\sqrt{66}}{40}
$