3.75x^2-36x+54=0

Solution for 3.75x^2-36x+54=0 equation:

3.75x^2-36x+54=0

a = 3.75; b = -36; c = +54;
Δ = b2-4ac
Δ = -362-4·3.75·54
Δ = 486
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:

$\sqrt{\Delta}=\sqrt{486}=\sqrt{81*6}=\sqrt{81}*\sqrt{6}=9\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-9\sqrt{6}}{2*3.75}=\frac{36-9\sqrt{6}}{7.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+9\sqrt{6}}{2*3.75}=\frac{36+9\sqrt{6}}{7.5}
$