X^2-24x=-119

Solution for X^2-24x=-119 equation:

X^2-24X=-119

We move all terms to the left:

X^2-24X-(-119)=0

We add all the numbers together, and all the variables

X^2-24X+119=0

a = 1; b = -24; c = +119;
Δ = b2-4ac
Δ = -242-4·1·119
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10}{2*1}=\frac{14}{2}
=7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10}{2*1}=\frac{34}{2}
=17
$