12x^2-72x+105=0

Solution for 12x^2-72x+105=0 equation:

12x^2-72x+105=0

a = 12; b = -72; c = +105;
Δ = b2-4ac
Δ = -722-4·12·105
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12}{2*12}=\frac{60}{24}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12}{2*12}=\frac{84}{24}
=3+1/2
$