6x^2-65x+125=0

Solution for 6x^2-65x+125=0 equation:

6x^2-65x+125=0

a = 6; b = -65; c = +125;
Δ = b2-4ac
Δ = -652-4·6·125
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-35}{2*6}=\frac{30}{12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+35}{2*6}=\frac{100}{12}
=8+1/3
$