12x^2-240x+90=0

Solution for 12x^2-240x+90=0 equation:

12x^2-240x+90=0

a = 12; b = -240; c = +90;
Δ = b2-4ac
Δ = -2402-4·12·90
Δ = 53280
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:

$\sqrt{\Delta}=\sqrt{53280}=\sqrt{144*370}=\sqrt{144}*\sqrt{370}=12\sqrt{370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-12\sqrt{370}}{2*12}=\frac{240-12\sqrt{370}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+12\sqrt{370}}{2*12}=\frac{240+12\sqrt{370}}{24}
$