x^2-24*x+118=0

Solution for x^2-24*x+118=0 equation:

x^2-24x+118=0

a = 1; b = -24; c = +118;
Δ = b2-4ac
Δ = -242-4·1·118
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{26}}{2*1}=\frac{24-2\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{26}}{2*1}=\frac{24+2\sqrt{26}}{2}
$