12x^2-320x+1500=0

Solution for 12x^2-320x+1500=0 equation:

12x^2-320x+1500=0

a = 12; b = -320; c = +1500;
Δ = b2-4ac
Δ = -3202-4·12·1500
Δ = 30400
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:

$\sqrt{\Delta}=\sqrt{30400}=\sqrt{1600*19}=\sqrt{1600}*\sqrt{19}=40\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-40\sqrt{19}}{2*12}=\frac{320-40\sqrt{19}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+40\sqrt{19}}{2*12}=\frac{320+40\sqrt{19}}{24}
$