-3x^2+12x-11.25=0

Solution for -3x^2+12x-11.25=0 equation:

-3x^2+12x-11.25=0

a = -3; b = 12; c = -11.25;
Δ = b2-4ac
Δ = 122-4·(-3)·(-11.25)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-3}{2*-3}=\frac{-15}{-6}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+3}{2*-3}=\frac{-9}{-6}
=1+1/2
$