51x^2-192x+180=0

Solution for 51x^2-192x+180=0 equation:

51x^2-192x+180=0

a = 51; b = -192; c = +180;
Δ = b2-4ac
Δ = -1922-4·51·180
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{-(-192)-12}{2*51}=\frac{180}{102}
=1+13/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+12}{2*51}=\frac{204}{102}
=2
$