x2=24x+50

Solution for x2=24x+50 equation:

x2=24x+50

We move all terms to the left:

x2-(24x+50)=0

We add all the numbers together, and all the variables

x^2-(24x+50)=0

We get rid of parentheses

x^2-24x-50=0

a = 1; b = -24; c = -50;
Δ = b2-4ac
Δ = -242-4·1·(-50)
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{194}}{2*1}=\frac{24-2\sqrt{194}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{194}}{2*1}=\frac{24+2\sqrt{194}}{2}
$