48x^2-192x+45=0

Solution for 48x^2-192x+45=0 equation:

48x^2-192x+45=0

a = 48; b = -192; c = +45;
Δ = b2-4ac
Δ = -1922-4·48·45
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-168}{2*48}=\frac{24}{96}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+168}{2*48}=\frac{360}{96}
=3+3/4
$