4x^2-120x+819=0

Solution for 4x^2-120x+819=0 equation:

4x^2-120x+819=0

a = 4; b = -120; c = +819;
Δ = b2-4ac
Δ = -1202-4·4·819
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-36}{2*4}=\frac{84}{8}
=10+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+36}{2*4}=\frac{156}{8}
=19+1/2
$