12x^2-65x+78=0

Solution for 12x^2-65x+78=0 equation:

12x^2-65x+78=0

a = 12; b = -65; c = +78;
Δ = b2-4ac
Δ = -652-4·12·78
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{481}}{2*12}=\frac{65-\sqrt{481}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{481}}{2*12}=\frac{65+\sqrt{481}}{24}
$