x2-48x+119=0

Solution for x2-48x+119=0 equation:

x2-48x+119=0

We add all the numbers together, and all the variables

x^2-48x+119=0

a = 1; b = -48; c = +119;
Δ = b2-4ac
Δ = -482-4·1·119
Δ = 1828
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:

$\sqrt{\Delta}=\sqrt{1828}=\sqrt{4*457}=\sqrt{4}*\sqrt{457}=2\sqrt{457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{457}}{2*1}=\frac{48-2\sqrt{457}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{457}}{2*1}=\frac{48+2\sqrt{457}}{2}
$