x^2-6x+6.75=0

Solution for x^2-6x+6.75=0 equation:

x^2-6x+6.75=0

a = 1; b = -6; c = +6.75;
Δ = b2-4ac
Δ = -62-4·1·6.75
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{-(-6)-3}{2*1}=\frac{3}{2}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+3}{2*1}=\frac{9}{2}
=4+1/2
$