3x^2-130x+100=0

Solution for 3x^2-130x+100=0 equation:

3x^2-130x+100=0

a = 3; b = -130; c = +100;
Δ = b2-4ac
Δ = -1302-4·3·100
Δ = 15700
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:

$\sqrt{\Delta}=\sqrt{15700}=\sqrt{100*157}=\sqrt{100}*\sqrt{157}=10\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-10\sqrt{157}}{2*3}=\frac{130-10\sqrt{157}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+10\sqrt{157}}{2*3}=\frac{130+10\sqrt{157}}{6}
$