6x^2-102x+320=0

Solution for 6x^2-102x+320=0 equation:

6x^2-102x+320=0

a = 6; b = -102; c = +320;
Δ = b2-4ac
Δ = -1022-4·6·320
Δ = 2724
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:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{681}}{2*6}=\frac{102-2\sqrt{681}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{681}}{2*6}=\frac{102+2\sqrt{681}}{12}
$