6x^2-100x+10=0

Solution for 6x^2-100x+10=0 equation:

6x^2-100x+10=0

a = 6; b = -100; c = +10;
Δ = b2-4ac
Δ = -1002-4·6·10
Δ = 9760
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:

$\sqrt{\Delta}=\sqrt{9760}=\sqrt{16*610}=\sqrt{16}*\sqrt{610}=4\sqrt{610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{610}}{2*6}=\frac{100-4\sqrt{610}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{610}}{2*6}=\frac{100+4\sqrt{610}}{12}
$