6x^2-20x+15=0

Solution for 6x^2-20x+15=0 equation:

6x^2-20x+15=0

a = 6; b = -20; c = +15;
Δ = b2-4ac
Δ = -202-4·6·15
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{10}}{2*6}=\frac{20-2\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{10}}{2*6}=\frac{20+2\sqrt{10}}{12}
$